Do Parents Tax Their Children? Teenage Labour Supply and ...

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Do Parents Tax Their Children?Teenage Labour Supply and Financial Support

IZA DP No. 10040

July 2016

Angus Holford

Do Parents Tax Their Children?

Teenage Labour Supply and Financial Support

Angus Holford ISER, University of Essex

and IZA

Discussion Paper No. 10040 July 2016

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IZA Discussion Paper No. 10040 July 2016

ABSTRACT

Do Parents Tax Their Children? Teenage Labour Supply and Financial Support*

This paper models child employment and parental pocket money decisions as a non-cooperative game. Assuming that the child human capital is a household public good and that the relationship between child human capital and employment is concave, we compare the welfare obtained under different decision-making mechanisms and test the predictions of the model for a cohort of English teenagers in compulsory education. Our results support a situation in which parents ‘tax’ their children’s earnings, withdrawing financial support as the child increases his working hours. This strategy forces the child to internalise the social cost of his activities. JEL Classification: C52, C72, D13, J22 Keywords: intra-household transfers, pocket money, child labour supply,

noncooperative game, human capital Corresponding author: Angus Holford Institute for Social and Economic Research University of Essex Wivenhoe Park Colchester, CO4 3SQ United Kingdom E-mail: [email protected]

* This work was carried out during PhD studies supported by an Economic and Social Research Council ‘1+3’ studentship in Economics [reference number ES/I025499/1], and postdoctoral research supported by the Economic and Social Research Council Research Centre on Micro-Social Change [reference number ES/L009153/1]. Thanks in particular for advice from supervisors and colleagues Emilia Del Bono, Stephen Pudney and Matthias Parey, and my PhD examiners Pedro Carneiro and Thomas Crossley, as well as seminar participants at Essex, the Family Economics Workshop at Royal Holloway, and the IZA Summer School in Labour Economics. All errors are my own. This work is based on data from the Longitudinal Study of Young People in England (Secure Data Service Access), produced by the Department for Education and National Centre for Social Research, and supplied through the Secure Data Service at the UK Data Archive. This work also uses local labour market statistics produced by the Office for National Statistics. The data are crown copyright and reproduced with the permission of the controller of the HMSO and Queens’s Printer for Scotland. The use of the data in this work does not imply the endorsement of the Department for Education, National Centre for Social Research, ONS, or Secure Data Service at the UK Data Archive in relation to the interpretation or analysis of these data.

IZA Discussion Paper No. 10040 July 2016

NON-TECHNICAL SUMMARY

Young adults who are still living with their parents and still in compulsory education finance their independent consumption using either parental transfers (pocket money), or by working part-time. Parents care about their own and their children’s consumption, but also about the effect that part-time work might have on their children’s study time and academic achievement, so are prepared to sacrifice some of their income to subsidize their children’s expenses. This paper investigates how parents and their teenage children interact to set the amounts of (i) pocket money and (ii) part-time work. We use data on part-time working hours, and pocket money from parents, reported by around 5000 girls and 5000 boys in compulsory education in England, interviewed annually between 2004 (when they were 14) and 2006 (when they were 16). At age 14, 25% of boys but only 19% of girls had a part-time job. By age 16, girls had overtaken (32% against 29%) but were earning slightly lower wages for similar hours (£4.06 against £4.34 per hour, both for about 6.5 hours a week). The propensity to offer regular allowances from parents was very similar for boys and girls, at around 80% over this period. Children take into account the money they get from parents when deciding whether to work or not. At age 14 they are 10-15 percentage points less likely to work if they are receiving an allowance, and this gap increases to 20 percentage points by age 16. Similarly, parents are around 15 percentage points less likely to give an allowance if their child is in paid work. Our empirical analysis of parents’ and children’s behaviour reveals two key findings. The first is that, other things equal, parents are more likely to give regular pocket money to teenagers who will have a harder time finding a job. This includes teenagers who are younger within their academic year at school so at a disadvantage when vacancies arise in the autumn, both before the run-up to Christmas and when older cohorts leave for university; those living in areas with higher rates of adult unemployment; and those living in areas from which the nearest shops are less accessible. This tells us that rather than being opportunistic (“these parents don’t need to pay their children not to work, so they don’t”), parents effectively ‘insure’ their child’s independent consumption against labour market difficulties outside their control. They would like them to finance their own personal spending money, but will not penalize them if this proves difficult. The second is that parents are less likely give regular pocket money to teenagers, the longer the teenager’s hours of part-time work. In other words, parents effectively tax their children’s earnings from part-time work, by taking away cash they would otherwise be handing over. This effect is larger for girls than boys and strongest when they are 16 years-old. We suggest that close to the high-stakes GCSE exams, which determine these children’s future educational and labour market opportunities, parents become more inclined to use their financial resources to reduce their child’s incentive to work, hoping they will spend more time studying instead.

1 Introduction

As teenagers become older they increasingly demand independence over their consumption and

time use (Dauphin et al., 2011). However, while remaining in compulsory education they are

dependent on in-kind or financial transfers from parents to support their living expenses. They

may also undertake part-time work in the labour market. Many do. The data used here shows

that around 25% of 13-16 year-olds below the minimum school leaving age in England have a job

during school term time. In the US, employment rates are considerably higher: approximately

60% for 14-15 year-olds (Buscha et al., 2008, Bureau of Labor Statistics, 2000), with 92% of

the National Longitudinal Study of Youth (NLSY) 1997 cohort having worked at some point

during High School (Hotz et al., 2002).

Having a job while still at school may improve teenagers’ welfare by affording them additional

independent consumption, and potentially improves their stock of human capital in the form

of financial literacy, communication skills and lower discount rates (Oettinger, 1999; Light,

2001). Conversely, by crowding out time and effort devoted to education, in-school employment

may impair the child’s academic performance and subsequent educational or labour market

opportunities (Ruhm, 1997, Department for Children, Schools and Families, 2009). Above a

moderate number of hours per week the latter effect has been shown to dominate. This critical

threshold also becomes lower, the closer to exam time (Lillydahl, 1990; Payne, 2004).

Being unable to earn a living wage, teenagers in full-time compulsory education have no ‘outside

option’ or bargaining power within the household (McElroy and Horney, 1981; Browning and

Chiappori, 1998). In this environment, it is convenient to abstract from the child’s actions

and preferences when modelling the household’s decision-making processes. Several studies

either implicitly invoke Becker’s (1974, 1981) ‘rotten kid theorem’, assuming the existence of an

altruistic head-of-household who is able to transfer resources among household members and so

(under certain conditions - Bergstrom, 1989; Ermisch, 2003) automatically induce the child to

maximise household utility (Bingley and Walker, 2013), or treat children as goods rather than

agents (Bourguignon, 1999; Blundell et al., 2005). When teenagers are able to take part-time

employment these characterisations are less easily supported. The child’s labour market activity

increases the household’s full income, but also either contributes to or reduces the child’s level of

human capital, which in the presence of an altruistic parent can be treated as a household public

good. This situation is similar to the time allocation decision faced by a couple over labour

1

supply and household production, wherein the free rider problem leads to underprovision of the

public good (Konrad and Lommerud, 1995). Assuming the parent has a lower discount rate

than the child (Burton et al., 2002), making her paternalistic or impurely altrustic, she will

weight the child’s human capital more heavily relative to the child’s consumption than will the

child himself. The child’s labour market activity therefore creates an externality: the ‘rotten

kid theorem’ does not apply because in the absence of a specific mechanism design the child

will work too many hours and produce too little human capital, relative to the (parent’s) social

optimum.

In this paper we identify the decision-making process governing parent-child interactions in

respect of the child’s part-time labour supply. We consider three ways in which parents can

use their financial resources to alter their child’s incentive to get a job. They can set a fixed

transfer level taking the child’s decision as given (a Nash equilibrium), or announce their transfer

in advance of the child’s decision (a parent-leading Stackelberg model), or withdraw transfers

in response to the child’s employment (a child-leading Stackelberg model).

The former two models assume that children take their parents’ transfer level as given when

making their labour supply choice. This is the most common assumption so far adopted in the

literature. Dustmann et al. (2009), using data on UK 14-15 year-olds in 1974, show children’s

labour supply is highly responsive to parental transfers, with an income elasticity similar to that

of adults. Gong (2009) (with data on US 12-16 year-olds in 1997) and Kalenkoski and Pabilo-

nia (2010) (US college students between 1997 and 2003) found a significant but more modest

elasticity. Wolff (2006), analysed French young adults aged 16-22 in 1992 and found no effect.

As well as providing new evidence for a recent UK cohort (14-16 year olds in 2004-2006), we

extend this literature by explicitly considering the implications of an impurely altruistic parent

who cares relatively more about the child’s human capital, and by exploring the implications

of the child-leading Stackelberg model, in which parents set a contingent transfer schedule, as

a potential alternative decision making process. This model implies that parents effectively tax

their child’s earnings.

As noted by Kooreman and Kapteyn (1990), a problem for applied work on household labour

supply is that it is not clear which theoretical model to implement empirically, and Apps and

Rees (1996) show that estimating misspecified models of intra-household income and labour

supply interactions can result in highly misleading inference. We address this key identification

2

problem by inferring the decision-making process used by households in two stages. First we

analyse the welfare implications of each model in a theoretical framework, then we take testable

predictions from each model to the data. This approach contrasts with other work in which the

decision-making process for parent-child interactions has been elicited directly (Lundberg et al.,

2009), which carries the potential for responses to to be driven by social desirability (Conti and

Pudney, 2011) or for households’ arrangements to be tacit rather than explicit, making answers

unreliable.

In our first step we show that with an impurely altruistic parent the Nash equilibrium is Pareto-

dominated, and so should be rejected on welfare grounds: both the parent and the child will

always be better off at a Stackelberg equilibrium. However, the parent-leading and the child-

leading Stackelberg models are non-nested and neither is a priori welfare-superior, so we then

test predictions derived from these models using data from the Longitudinal Study of Young

People in England (LSYPE). The parent leading Stackelberg would predict that parents are

opportunistic in terms of reducing financial transfers in response to factors restricting the child’s

work opportunities, but we instead show that parents insure their child’s consumption against

labour market difficulties outside their control (Ermisch, 2003, p.5). Our results are consistent

with a decision-making process in which parents ‘tax’ their children’s earnings, withdrawing

financial support as child labour supply increases. This is in line with the predictions of the

child-leading Stackelberg model.

While there is strong evidence about the primacy of the role of parents in promoting financial

literacy and financial socialization of young adults, outweighing the contributions from part-time

work or from formal education (Shim et al., 2010), giving pocket money alone (characteristic of

the Nash and parent-leading Stackelberg models) is shown to be ineffective for stimulating adult

savings (Bucciol and Veronesi, 2014). Our finding shows that parents combine their giving of

pocket money with communication about a trade-off teenagers face when making an important

financial decision, which is an encouraging model for promoting the the financial literacy of

young adults.

We make an additional contribution to the empirical literature by repeating our analysis on the

same cross-section of parents and children in successive years. This enables us to evaluate how

the parameters of the model change as teenagers get older, while holding constant the other

factors (country, education level, era) collectively driving the differences between the labour

3

supply and transfer elasticities seen in the earlier literature. In particular, we show a significant

increase in the propensity of parents to ‘tax’ the part-time earnings of girls during their final

year of compulsory schooling when high stakes GCSE examinations are taken over earlier years.

This is consistent with parents using their financial resources to discourage part-time work,

during the periods when the opportunity cost of part-time work is highest.

2 Theoretical Model

Our model assumes two agents, a selfish child and an altruistic parent. The child cares about

his own consumption (C) and his own human capital (H). The parent cares about her own

consumption (P ), the child’s consumption, and the child’s human capital. The utility functions

depend on each agent’s relative preference for child’s human capital over child’s consumption,

denoted κc (child) and κp (parent). Here we assume that the parent’s altruism is impure or

paternalistic, meaning that κp > κc. Each agent’s κ is a predetermined function of exogenous

individual and household preferences and characteristics, X, so κi = κi(X) for i = p, c. The

utility functions can be written U c = U c(C,H, κc(X)) (child) and Up = Up(C,P,H, κp(X))

(parent). Both are three times continuously differentiable in C, P and H; strictly increasing in

C, P and H at a dimishing rate; and separable in C, P and H, such that the marginal utility

from each element is independent of the other elements.1

Prior to making his labour supply decision, the child has a baseline endowment of human capital,

µ. This is also a predetermined function of X, so µ = µ(X). These current and past parental,

child and household characteristics are assumed to have determined the parent and child’s time

and effort devoted to investment activities over the preceding lifecourse. The child’s human

capital accumulation in a given period is also a function of his time devoted to wage-earning

employment L, so H = H(L, µ). We assume that the marginal human capital product (HL)

of the first hour of labour supply can be positive or negative, but (HL) is decreasing in L

(so HLL < 0). This captures the idea that beyond some level of hours of work employment

must detract from the quality or quantity of time devoted to other human-capital earning

pursuits. This is consistent with the findings of Ruhm (1997), Tyler (2003) and Montmarquette

et al. (2007), among others, and we assume that this stylised fact is built into individuals’

1Formally, the restrictions on the child’s utility function are: UcC > 0; Uc

CC < 0; UcH > 0; Uc

HH < 0; UcCH = 0.

The restrictions on the parent’s utility function are: UpC > 0; Up

CC < 0; UpP > 0; Up

PP < 0; UpH > 0; Up

HH < 0;U

pPH = 0; Up

PC = 0; UpHC = 0.

4

expectations.

In our model, the parent has exogenous income M , and can choose to transfer the cash amount

t ≥ 0 to the child. The parent consumes the rest of her income, so P = M − t. The child

chooses his labour supply, L, and earns the constant wage w > 0. His consumption is the sum

of labour earnings wL, and money received from parents: C = wL+ t.

Observed transfer and labour supply behaviour represents the solution to the one-shot game

in which the parent and child each maximise their own utility in the current period subject to

their preferences and production function of human capital.

We assume that parents and children do not have a mechanism for a complete, binding commit-

ment. This means we adopt a non-cooperative model. This is supported by empirical evidence

showing there is imperfect communication between the parent and child during adolescence, a

period in which young people establish their identity and develop the ability to make their own

decisions (Collins, 1990). As Lundberg et al. (2009) put it, “effective information exchange

[is] hampered by the [child’s] still-developing cognitive and communicative abilities”. These

communication difficulties stem from both the asymmetric relationship between parents and

adolescents and divergent expectations about the child’s autonomy (Steinberg, 2001; Collins

and Luebker, 1994), and from the changing nature of the relationship over time (Collins et

al, 1997), leading to an unstable bargaining environment (“constantly changing as the child

matures”; Lundberg et al., 2009).

In our theoretical model, we follow Burton et al. (2002) and Schmidt (1993) by assuming that

the parent has developed a reputation and the child’s discount rate is sufficiently high that

he takes the parent’s strategy (though not necessarily action) as given in each period. We

then build on two subsequent approaches to modelling household labour supply adopted in the

earlier literature (see Apps and Rees, 2009, pp.75-76, for a discussion). Firstly we model the

child’s consumption and human capital as a household public good, and secondly we derive and

identify best response functions for both agents’ decision variables (Antman, 2012; Leuthold,

1968; Ashworth and Ulph, 1981).

In the following sections will derive the unique equilibrium under (i) the Nash decision-making

process, (ii) the parent-leading Stackelberg model, and (iii) child-leading Stackelberg model.

This final model can also be framed as the parent setting a contingent transfer schedule.

5

2.1 Nash and Stackelberg equilibria

In a Nash framework, the parent and child choose their cash transfer and labour supply as

their best response to the other’s action. At the Nash equilibrium, neither agent can do better,

taking the other’s action as given. Implicitly, this position is reached by a myopic adjustment

procedure or iterative process in which the agents choose starting positions and best-respond

in turn to converge on the equilibrium (Leonard, 1994). In the Stackelberg framework, one

party ‘leads’ by committing to the action that maximises their own utility taking into account

that the other agent will ‘best respond’ to the leader’s actions. Here, there are two Stackelberg

equilibria, one in which the parent leads and one in which the child leads.

In the parent-leading Stackelberg model, the parent fixes the cash transfer in advance. The

child follows with his best response in terms of employment, taking the cash transfer as given.

We assume the parent can costlessly and rapidly alter the transfers. However, this flexibility

threatens the parent’s credibility or time-consistency. A Stackelberg equilibrium requires the

follower to believe the leader will not deviate from her initial action. In an application of the

‘Samaritan’s Dilemma’ (Bruce and Waldman, 1991; Lindbeck and Weibull, 1988) this means

that the parent must hold the transfer level fixed in case of the child being involuntarily un-

employed or under-employed, and that parental transfers do not respond to changes in labour

market conditions.

In the child-leading Stackelberg model, the child anticipates the parent’s best response and

‘leads’ by choosing his employment level. The parent then follows with his best response in terms

of cash transfers, taking the employment level as given. We assume the parent has deterministic

control over cash transfers. This means the child’s first-move commitment will not come under

challenge due to the parent deviating from her expected best-response for reasons outside her

control. The child’s labour supply decision is less reversible than the parent’s transfer decision.

The child can leave a job but not easily find another job or adjust his hours. These considerations

mean the employment level is more likely to represent a credible, binding commitment than the

transfer level.

The parent’s relative financial resources, lower discount rate, and position of authority within

the household, and the child’s lack of an outside option should all mean the parent has all of the

bargaining power (McElroy and Horney, 1981; Browning and Chiappori, 1998). The idea of a

child-leading Stackelberg model, in which the parent ‘does the best she can given the action of

6

a dominant child’ is therefore not intuitively appealing. However, this scenario can be reframed

as the parent announcing a contingent schedule of transfers that will be made for every possible

level of employment the child can take, and the child choosing the point along it which is best

for him. Note that with a fully contingent strategy, there is no time-consistency problem for

the parent.

Hence, both the parent-leading and child-leading Stackelberg models are consistent with a

situation in which the parent has the bargaining power and chooses the decision-making process.

We assume she chooses that which her best off (Bell et al., 2012). We now evaluate the welfare

outcomes of the three possible models.

2.2 Comparing the outcomes of alternative models

Each agents’ optimisation problem can be illustrated graphically in a utility map in the [transfer,

labour supply] space, as shown in Figure 1.

Here, the child has a ‘bliss point’ (point of maximum utility) at infinite transfers and the

human capital maximising level of labour supply. The child’s best response correspondence,

BRc = L∗(t, w,X), is the locus of points maximising the child’s utility for each given transfer

level. This passes through the turning point of each indifference curve (U c1 , U

c2 , etc). Above

the BRc, the indifference curve is upward sloping: the marginal human capital cost of working

is so high that he requires additional transfers from the parent as well as his own earnings to

compensate for it.

As the parent cares relatively more about human capital than does the child, the parent’s ‘bliss

point’ lies below the child’s best-response correspondence. If the parent is very selfish, the high

cost in terms of her own consumption of increasing the child’s human capital and consumption

will result in a bliss point below the human-capital maximising level of labour supply. The

parent’s best response correspondence BRp = t∗(L,M,X) is the locus of points maximising the

parent’s utility for each given labour supply. This passes through the maximum and minimum

points of her concentric indifference curves (Up1 , U

p2 , etc). These carry decreasing utility coming

from suboptimal consumption allocations when increasing or decreasing transfers either side of

the bliss point, and reduced human capital when increasing labour supply above, or reducing

below, the human capital maximising level.

Although next we will set out each agents’ optimality conditions and the resulting welfare

7

Figure 1: Agents’ optimisation problem and the three equilibria

Parent

bliss

point Human

cap’ max’

0 → t t

L

↑

0

L

= t*(L, M, X)

= L*(t, w, X)

Child bliss

point at

t=∞

Nash equilibrium

Child-leading

Stackelberg

equilibrium

Parent-leading

Stackelberg

equilibrium

Increasing child’s utility

Increasing parent’s utility

comparisons formally, this utility map shows the intuition for a straightforward interior solution

case. The Nash equilibrium, or mutual best response, is at the intersection of the agents’ best-

response correspondences. Both Stackelberg equilibria entail the leader choosing the point on

the follower’s BR correspondence which makes him or her best off.2

2.2.1 Nash versus parent-leading Stackelberg

The parent’s maximisation problem is the same under a Nash equilibrium as when she acts as

a Stackelberg follower. In either case, when choosing her transfer level she takes the child’s

labour supply L as given:

maxt

Up = Up(P (M − t), C(wL+ t), H(L, µ(X), κp(X)) (1)

2Figure 1 shows an interior solution. Because transfers must be non-negative, if at t = 0 the parent’s marginalutility from her own consumption exceeds that from the child’s human capital and consumption, she will make zerotransfers. If the human capital maximising level of labour supply is L = 0 and for the first hour of employmentthe child’s marginal utility lost from human capital is greater than that gained from increased consumption, thechild will work zero hours.

8

and her optimality condition is:

UpC = U

pP (2)

This states that the parent will make transfers to the point where her marginal utility from (i)

her own consumption, and (ii) the child’s consumption and human capital, are equal. This will

occur at a maximum or minimum point of a parental indifference curve.

Acting as a Stackelberg leader, the parent’s maximisation problem must account for the indirect

effects of t on her utility from the child’s consumption and human capital, caused by the child’s

labour supply response to t:

maxt

Up = Up(P (M − t), C(wL∗(t) + t), H(L∗(t), µ(X)), κp(X)) (3)

Her optimality condition is now:

UpC +

∂L∗

∂t[Up

C · w + UpH ·HL] = U

pP (4)

She still makes transfers to the point where the marginal utilities from her own consumption

and the child’s consumption and human capital are equal, but this time accounting for the

child’s optimal labour supply response. This means she chooses the point on the child’s BR

correspondence that is tangent to a parental indifference curve. This will represent the parent’s

highest attainable utility under this framework.

The expression in square brackets in equation (4) is similar to the child’s Stackelberg-leading

optimality condition (equation 9, below): w.U cC = −HL.U

cH , or equivalently w·U c

C+HL ·UcH = 0.

Both expressions are equal to the net change in the parent’s utility caused by simultaneous

changes in the child’s consumption and human capital. If the parent were purely altruistic,

placing the same relative weight on the child’s human capital and consumption as does the

child, then [UpC · w + U

pH ·HL] and [U c

C · w + U cH ·HL] would both equal zero at the same level

of labour supply and transfers. This would mean the parents’ bliss point lies on the child’s BR,

and the Nash and parent-leading Stackelberg equilibria would coincide, as shown by Dustmann

et al. (2009). As we assume that the parent’s altruism is paternalistic however, at the Nash

9

level of transfers it holds that UpC · w + U

pH ·HL < 0, and hence:

UpC +

∂L∗

∂t[Up

C · w + UpH ·HL] > U

pP (5)

From this position, in the Stackelberg model, the parent’s paternalism makes her prepared to

pay the child more (increase t) to persuade him to work less (reduce L).3 It can be shown that

the child’s BR is sufficiently shallow for him always to withdraw labour earnings at a slower rate

than transfers are received (see Appendix A.3.1, page 53, for the complete derivation) and both

equilibria must lie in the range where the marginal human capital product of labour is negative

(HL < 0). Otherwise, the child and parent would always prefer to increase labour supply at

the benefit to both human capital and consumption. Hence, both the child’s consumption and

human capital must be higher at the parent-leading Stackelberg equilibrium than at the Nash

equilibrium. Moving from the Nash to the parent-leading Stackelberg equilibrium makes both

the parent and the child better off.

2.2.2 Nash versus child-leading Stackelberg

The child’s maximisation problem when choosing his labour supply is the same under a Nash

equilibrium as when he acts as a Stackelberg follower. In both cases, he takes the transfer, t,

made by the parent, as given:

maxL

U c = U c(C(wL+ t), H(L, µ(X)), κc(X)) (6)

and his optimality condition is:

w.U cC = −HL.U

cH (7)

meaning his marginal utility from additional consumption (his gross wage) is equal to that from

foregone human capital.

Acting as a Stackelberg leader the child’s optimisation problem is as follows:

maxL

U c = U c(C(wL+ t∗(L)), H(L), µ(X), κc(X)) (8)

3In Appendix A.1 (page 44) we consider the implications of a parent with a different kind of impure altruisticpreferences: those who derive no utility from the child’s human capital.

10

and his optimality condition is:

(w +∂t∗

∂L) · U c

C = −HL · U cH (9)

The parent withdraws transfers in response to increasing labour supply, so ∂t∗

∂L< 0, meaning

that when acting as a Stackelberg leader, the child instead bases his labour supply on his net

wage (w + ∂t∗

∂L) rather than gross wage. He selects the point on his parents’ best response

correspondence, which he can view as a contingent tax or transfer schedule, which gives him

highest utility. This will occur at a tangent point to a child indifference curve. Formally, at the

Nash level of labour supply it holds that:

(w +∂t∗

∂L) · U c

C < −HL · U cH (10)

At this position, the net wage is too small to compensate the child for the marginal human

capital cost of employment. He will therefore reduce his labour supply, raising his human

capital and reducing consumption, but become better off overall.

At equilibrium, the ‘tax rate’ - the slope of the best-response correspondence along which

cash transfers from parents are observed to be withdrawn in response to the child’s earnings - is

strictly between zero and one (see Appendix A.3.2, page 54, for the complete derivation). Above

the human capital maximising labour supply, the child will never work for a negative or zero net

wage, and the equilibrium cannot occur at a point where the parent is subsidizing the child’s

employment. The parent only does this where (i) the child’s human capital is still increasing

in labour supply or (ii) where she would prefer to increase the child’s consumption at the cost

of reducing her own consumption and her child’s human capital. The parent’s ‘bliss point’ will

occur at the point where the parent is indifferent between increasing the child’s consumption,

reducing the child’s human capital, and reducing her own consumption. In this state she

will neither tax nor subsidise the child’s employment. Hence, the child-leading Stackelberg

equilibrium must lie at a point on the parent’s best-response correspondence between the Nash

equilibrium and the parent’s bliss point. This means that both the child and the parent are

better off at the child-leading Stackelberg equilibrium than the Nash equilibrium.4

4It is a sufficient condition for this welfare improvement that the parent’s preferences are paternalistic. Onemay also consider that if the child-leading Stackelberg equilibrium lay below the parent’s bliss point, it wouldimply that while the child is happy with the trade-off between human capital and consumption, the parent wouldprefer to raise the child’s consumption and reduce his human capital. This would violate our assumption that

11

2.3 The identification problem

If the chosen decision-making process were known, the strategy for identifying each agent’s

BR correspondence can easily be visualised in Figure 1. In the Nash framework, each agent’s

BR correspondence is traced out by shifts in the other’s BR correspondence, caused by factors

having no direct effect on their own. In each Stackelberg model, shifts in the leader’s utility

map caused by factors having no direct effect on the follower’s BR will trace out this BR as the

locus of points which are tangent to the leader’s highest attainable indifference curve.

However, the chosen decision-making process is ex ante unknown, and estimating misspecified

models of intra-household income and labour supply interactions has been shown to result in

highly misleading inference (Apps and Rees, 1996). Following Apps and Rees’ approach, our

identification problem can be illustrated by considering the result we would obtain were we to

proceed under the belief that the Nash framework was the correct specification for household

behaviour when the true data generating process the is parent-leading Stackelberg model. Then,

shifting the child’s BR correspondence will trace out a locus of points which are tangent to the

parent’s indifference curves. This will incorrectly be interpreted as representing the parent’s BR

correspondence. The case shown in Figure 2 would lead us to conclude that at the equilibrium

margin parents are choosing to subsidise, rather than tax, their child’s earnings.

To identify the decision-making process we follow first a theoretical and then an empirical

argument. We can rule out the observed outcomes ever representing the Nash equilibrium

on welfare grounds. We showed in section 2.2, and it is apparent in Figure 1, that both the

parent and the child are better off at both the parent-leading and the child-leading Stackelberg

equilibria, meaning the Nash equilibrium is Pareto dominated. The parent-leading model is

superior even for the child because the parent’s paternalism makes him prepared to pay the

child more to work less. The child-leading model is superior even for the parent because the

positive marginal tax rate faced by the child means he internalises the social cost (in terms of

human capital) of his employment. This makes him reduce his labour supply, which pleases the

parent.

We assume the parent chooses the decision-making process which gives her the highest utility.

Our theoretical framework cannot indicate whether this will be the parent-leading or child-

leading Stackelberg model. Figure 1 is drawn assuming that the parent is indifferent between

the parent cares relatively more about human capital than does the child.

12

Figure 2: Erroneous identification of the parent’s best response.

Parent

bliss

point

0 → t t

L

↑

0

L

Shifts in child’s

best response

= L*(t, w, X)

Child bliss

point at

t=∞

True parent’s

best response Estimated

parent’s best

response

Observed data

points are

Stackelberg

equilibria

= t*(L, M, X)

Human

cap’ max’

these decision-making processes, receiving utility level UP2 in both cases. The more paternal-

istic are the parent’s preferences (characterised by a steeper subsidy and tax on employment

below and above the parent’s bliss point respectively), the greater scope there is to favour the

child-leading model.5 The more selfish is the parent overall (characteristed by shifting her BR

correspondence to the left and her bliss point to a lower level of labour supply, and reduc-

ing the tax and subsidy rates over the relevant ranges), the more scope there is to favour the

parent-leading model.

Since we cannot reject either Stackelberg model on theoretical grounds, we must do so on empir-

ical grounds. We now discuss testable predictions derived from the parent-leading Stackelberg

model that allow us to validate or reject this model.

2.4 Labour market rationing and the Stackelberg model

The parent-leading Stackelberg model requires that the parent will hold transfers constant

in response to factors expected to restrict the child’s optimal choice (his labour supply or

5In Appendix A.1 we derive the predictions of the model for the extreme case in which the parent gains noutility from the child’s human capital. In this case, we show that the parent-leading model is strictly preferredto the Nash, in turn strictly preferred to the child-leading model.

13

probability of obtaining a job). Labour demand conditions should have no effect on the agents’

preferences or utility except via the child’s labour supply. Therefore, a time-consistent parent

should ignore these factors in setting his transfer decision.

In addition, if a binding ceiling is placed on the child’s hours of employment, then the parent

should reduce the transfers made to the child: she no longer needs to ‘pay the child not to

work’ and at this ceiling can reduce transfers without trading her rise in consumption against

a reduction in the child’s human capital. Such a ceiling may result from legal restrictions on

the number and timing of hours of employment a child may offer, or from labour demand

constraints.

If the parent-leading Stackelberg model is true, therefore, we should find that the effect of

the labour demand variables expected to restrict the child’s employment opportunities on the

transfer are either zero or negative. If this prediction is rejected empirically, the only decision-

making process left standing is the child-leading Stackelberg model, and we present results

which are fully consistent with this framework being used.

3 Data and institutional background

3.1 LSYPE data

We test the predictions of our model using data from the first three waves of the Longitudinal

Study of Young People in England (LSYPE). This sample is drawn from a single academic

cohort of teenagers in England, interviewed annually from 2004-2006 at age 14 (school year 9),

15 (year 10), and 16 (year 11), the last three years of compulsory schooling. The data enable us

to control for a rich set of individual and household variables and the child’s prior educational

performance.

The question on parental cash transfers is “Do you receive any pocket money, allowances, or

other support towards your living costs from parents or relatives?”. The emphasis on “al-

lowances” or “support towards your living costs” but without reference to specific items means

that this does not refer to hypothecated transfers. The present tense makes clear that this

unearned income refers to a current, ongoing, and regular arrangement that represents a close

substitute for labour income. Since we observe changes in parental transfers only at the ex-

tensive margin, switching from positive to zero transfers, we assume that this variable reflects

14

parents’ latent desired transfer level, and that this changes monotonically with parental income,

child labour supply, and child’s labour market restrictions.

Youth respondents are also asked “Do you ever do any work in a spare-time paid job, even

if it is only for an hour or two now and then? (Please don’t include jobs you only do during

the school holidays or voluntary work)”. Those answering ‘yes’ are asked “How many hours on

average do you usually work in this job (or jobs) during a term time week? Please include any

hours you work at the weekend during term-time”. These questions explicitly exclude unpaid

or voluntary work, ensuring that a positive response is unambiguously associated with labour

income. The term-time focus makes the crowding out of study time or other extra-curricular

activities a salient concern.

3.2 Employment of children in England

The rules governing the employment of children in England are set by the Department for

Education (see guidelines in DCSF, 2009). Children aged at least 13 but less than the school

leaving age may undertake ‘light’ work, deemed as not being harmful to their health, safety or

development.6 There are age-specific restrictions on the types and hours of work children may

do. Those under 16 cannot work ‘mainly or solely’ for the sale of alcohol, for example. Those

in compulsory education may work only 12 hours per week in term time, including a maximum

of 2 hours on a weekday or Sunday; 8 hours on a Saturday (5 hours if under 15 years); one hour

before school on a weekday; and none during school hours or after 7pm on a school night. Those

employing children below the school leaving age must obtain the signature of a parent and a

permit from the Local Education Authority, which must be satisfied that the child’s education

will not be damaged. Howieson et al. (2006) estimate that in Scotland only 11% of children

covered by this legislation had the required permit, so these regulations are poorly enforced.

3.3 Descriptive statistics

Table 1 shows descriptive statistics relating to employment, earnings and cash transfers from

parents. The propensity to work rises as the children age, particularly among girls, who start

from a lower base. Conditional on working, girls work longer hours than boys, but receive lower

6Full-time education is compulsory until the last Friday in June of the academic year when the child turns 16.

15

earnings and hourly wages. The proportion receiving cash transfers declines very slightly with

age, and is marginally higher for girls than boys.

Table 1: Descriptive statistics: Employment and transfer receipt by gender

Wave 1 (Age 14) Wave 2 (Age 15) Wave 3 (Age 16)

Boys Girls Boys Girls Boys Girls

Employed (%) 24.9 18.9 28.3 27.1 29.0 31.2

Receive cash transfer (%) 80.9 81.7 77.8 79.4 76.7 78.4

Mean hours employment2 4.14 4.24 5.16 5.38 6.44 6.72(conditional on being employed) (0.10) (0.11) (0.13) (0.10) (0.15) (0.13)

Mean earnings2, £s 14.52 14.24 20.58 18.90 27.96 27.31(conditional on being employed) (0.41) (0.39) (0.52) (0.33) (0.63) (0.55)

Observations 7116 7250 6258 6303 5815 5839

Notes: All figures for hours and earnings are weekly. Standard errors in parentheses. Population means and proportions calculated usingfinal probability weights. Standard errors clustered by school. 1: GCSE capped point score (calculated over best eight subjects). 2: Hours

of employment and earnings are per week. 3: Key Stage 3 Average Point Score, standardized by subtracting mean and dividing by standarddeviation.

Table 2 shows the differences in prior educational performance (age 14) and subsequent ed-

ucational performance (age 16) according to the child’s employment status in each year. At

every stage, and for both boys and girls, those in employment are positively selected on age

14 educational performance, and go on to perform better at age 16 by a sufficient margin to

widen future educational opportunities substantially.7 This relationship is driven by the posi-

tive correlation between factors determining employability and academic performance, such as

individual motivation, relative age (Plug, 2001; Crawford et al., 2013), school quality, parental

investments, and local labour market conditions.

Table 2 also shows that the gender wage gap is not driven by differential selection: Girls

have superior prior educational performance and are more positively selected into employment

according to these grades. Instead, these observations are consistent with boys and girls being

active in distinct labour markets with different wage rates and factors restricting employment:

Kooreman (2009) shows the in-school employment gender wage differential in the Netherlands

is due to the concentration of girls in babysitting roles, for example. For this reason we estimate

7The difference in performance is equivalent to one GCSE grade in four of the student’s best eight subjects.The threshold for continuation in full-time education is five A*-C grades. This is achieved by around 60% ofstudents. Students typically take around 10 GCSE courses.

16

Table 2: Descriptive statistics: Prior and subsequent educational performance by employmentstatus

..Wave 1 (Age 14).. ..Wave 2 (Age 15).. ..Wave 3 (Age 16)..


Standardized age 14 exam score3 by employment status

If employed 0.097 0.293 0.096 0.302 0.114 0.302(0.032) (0.034) (0.033) (0.031) (0.031) (0.034)

If not employed.......... -0.101 0.019 -0.090 -0.009 -0.094 -0.015(0.034) (0.030) (0.036) (0.018) (0.037) (0.034)

Mean age 16 exam score3 by employment status

If employed 294.31 328.06 295.07 331.37 299.44 334.50(3.35) (3.42) (3.47) (2.83) (2.83) (2.96)

If not employed.......... 276.75 303.62 277.41 301.36 276.39 300.91(3.50) (2.89) (3.57) (1.92) (3.69) (3.30)

Observations 7116 7250 6258 6303 5815 5839



our models separately for males and females.8

Finally, Table 3 shows that employment and financial support are always negatively correlated.

Parents are always more likely to make cash transfers to children who do not work, and chil-

dren are always more likely to work if they do not receive cash transfers. This is consistent

with children’s working decision being financially motivated and with parents’ use of financial

transfers to disincentivise child employment.

4 Estimation

We estimate cross-sectional models of the observed counterparts to the parent-leading and child-

leading Stackelberg models. The econometric specification for the transfer and labour supply

decisions are shown in equations (11-12) and (13-14). In this exposition the functions and error

terms with superscript S refer to an agent acting as a Stackelberg leader. The superscript N

refers to an agent taking the actions of the other as given, as in a Nash equilibrium or acting

8In addition to social norms about the types of jobs to be taken by boys and girls, there are rigid genderroles within certain ethnic groups which make employment among girls exceptionally rare, both in comparisonto other ethnic groups and to boys of the same ethnic group. Appendix A.4, page 56, presents some descriptivestatistics on both these topics.

17

Table 3: Descriptive statistics: Negative correlation between child’s part-time employment andparental transfers

.Wave 1 (Age 14). .Wave 2 (Age 15). .Wave 3 (Age 16).


Transfer receipt, %, by employment status:

If employed 71.5 73.3 66.3 71.1 63.2 67.5

If not employed 83.9 83.6 82.4 82.6 82.0 83.3

Employment rates, %, by transfer receipt

If receives transfers 22.0 17.0 24.2 24.3 23.1 26.8

If does not receive transfers..... 37.1 27.6 43.1 38.2 44.4 46.9

Observations 7116 7250 6258 6303 5815 5839



as a Stackelberg follower.

The decision to estimate separately by wave rather than exploiting the panel nature of this

dataset is made because the teenage years are a time of transition. Teenagers have very different

labour market opportunities at age 16 than 13. Time away from studying may be increasingly

costly in terms of educational performance the closer the children get to the exams which will

determine their future academic opportunities. Children will desire higher consumption and

increasing independence over what they consume. For these reasons, we do not expect a stable

relationship over time that conventional panel data methods are appropriate for.9 Moreover,

this approach enables us to identify the effect of changing one contextual factor - the age of the

children - on the parameters of the model. This is a key contribution to a literature in which

several factors may be responsible for differences in previous findings.

9We use longitudinal weights to ensure that the estimates are obtained from the same sample of individualsat each wave and that the sample is representative of the population in terms of household demographics andparental background as measured at wave 1. See James et al. (2010) for details of the weights’ construction.

18

4.1 Parent-leading Stackelberg model

Equations (11-12) show the parent-leading Stackelberg model. Equation (11) represents the

parent’s transfer decision. Equation (12) represents the child’s effective best correspondence.

t = 1 if tS(M,Z,X) + ǫSt > 0 (11)

t = 0 if tS(M,Z,X) + ǫSt ≤ 0

L = LN (tS ,Z,X) + ǫNL if LN (tS ,Z,X) + ǫNL > 0 (12)

L = 0 if LN (tS ,Z,X) + ǫNL ≤ 0

Transfers and labour supply are subject to correlated random shocks due to unobservable het-

erogeneity in preferences, resources, and constraints such as discrete job offers and variation in

travel time to school or work, such that:

(

ǫStǫNL

)

∼ N

(

00

)

,

(

σSt ρ1ρ1 σN

L

)

This system of a simultaneous probit and tobit is estimated using Full Information Maximum

Likelihood (FIML). This system is identified through the exclusion of parental income, M

from the second stage (child’s labour supply) equation. In other words, we assume that the

probability of receiving a transfer is strictly increasing in parental income, but there is no direct

effect of parent income on child’s labour supply (Dustmann et al., 2009; Wolff, 2006; Kalenkoski

and Pabilonia, 2010; and Gong, 2009).10

Variables expected to restrict the child’s labour market opportunities, Z are included in both

equations to enable us to test whether (i) these variables have the predicted effect on child

labour supply, and (ii) the parent holds constant or reduces transfers in response to these

labour demand conditions.

10The LSYPE uses a different measure of income in each sampling wave. In waves 1 and 3 the variable“Total income from work, benefits and anything else for [Main Parent] (and partner)” is elicited in 92 bandsand 12 bands respectively. In wave 2, the “gross annual salary” of both parents and the “total annual amountof benefits received” are elicited separately, and other sources of income are omitted. Because these measuresare not directly comparable, we use a ‘relative permanent income’ measure defined as the percentile (zero beingthe lowest, one being the highest) of the household’s mean gross income percentile across the three waves, usingimputed household income where necessary. Details of the imputation procedure can be found in James et al.(2010).

19

4.2 Child-leading Stackelberg model

Equations (13-14) show the child-leading Stackelberg model. Equation (13) represents the

child’s labour supply decision, with the child accounting for the parent’s transfer schedule.

Equation (14) represents the parent’s best response, or contingent transfer schedule:

L = LS(M,Z,X) + ǫSL if LS(M,Z,X) + ǫSL > 0 (13)

L = 0 if LS(M,Z,X) + ǫSL ≤ 0

t = 1 if tN (L,M,X) + ǫNt > 0 (14)

t = 0 if tN (L,M,X) + ǫNt ≤ 0

We again assume the presence of correlated random shocks such that:

(

ǫNtǫSL

)

∼ N

(

00

)

,

(

σNt ρ2ρ2 σS

L

)

This system is identified through the exclusion of labour market factors Z from the second-stage

(parental transfer) equation.

We use three different ways to represent restrictions on the child’s labour supply. First, the

child’s relative age within the academic cohort is included as a linear term, equal to 1 for

September birthdays (the oldest in the cohort) up to 12 for those born the following August.

Children born earlier in the academic year will be allowed to work longer hours or access specific

job types earlier than their younger peers. This means they are better placed to fill suitable

vacancies which arise in the autumn as temporary staff are taken on prior to Christmas, and

members of older cohorts move away to university. The parent’s attitude to financial support

may however change when the child turns a year older, so we also control for the child being

interviewed after their birthday within the academic year.

Secondly, we use the 2004 index of multiple deprivation (IMD) of the teenagers’ area of residence

as a proxy for very localized area characteristics determining a teenager’s employment oppor-

tunities. The IMD measures the prevalence of deprivation within geographical areas containing

400-1200 households (Office of the Deputy Prime Minister, 2004). The index is calculated from

20

aggregated individual-level deprivation indicators and area characteristics in seven domains:

income; employment; health; education, skills and training; barriers to housing and services;

crime; and the living environment. All these elements are expected to be correlated with youth

labour market opportunities. Of greatest relevance in driving this relationship are (i) the area

unemployment rate, and (ii) the average road distance to a post office and supermarket or con-

venience store. The latter are suitable potential employers and may also be clustered with other

shops and businesses. The IMD is functionally dependent on the characteristics of the individual

households observed in the LSYPE. To net out this effect we explicitly control for household-

level counterparts to the componenents of the aggregated deprivation indicators recorded in the

IMD. We assume that conditional on household circumstances (including parental employment

and income and the child’s prior educational performance) the local area characteristics cap-

tured by the IMD have no direct effect on the parent’s transfer decision except via the child’s

employment opportunities.

Thirdly, we use the adult (aged 16-64) unemployment rate in the youth’s local authority district

(LAD) of residence at time of interview. There are 325 LADs in England, with an average

population of 164,000. This variable therefore represents labour market opportunities over a

wider geographic area. Conditional on the parents’ own income and employment status we

assume this has no direct effect on parent’s transfer decision, except via the child’s employment

opportunities.

4.3 Additional controls

The vector of additional controls, X, includes further variables expected to affect the parent’s

resource constraints, either agent’s relative preference for human capital (κi) or the child’s

labour market opportunities or endowment of human capital (µ). These comprise (i) socio-

economic characteristics, including parent’s employment status and education; (ii) the child’s

prior educational performance and special educational needs (SEN) status; (iii) ethnicity dum-

mies, to account for differing preferences and labour market discrimination; and (iv) household

structure, which determines individual’ material and time resources as well as preferences. We

account for geographical and seasonal variation in labour market opportunities with dummies

for urban-rural status, residence outside Greater London, and year and month of interview.

21

5 Results

In this section, we first present the estimates obtained under the parent-leading Stackelberg

framework. We show these are contrary to the predictions of the model in two ways. We then

show results consistent with the child-leading Stackelberg mechanism being used instead. The

complete maximum likelihood estimation output for both sexes and all waves is presented is

Appendix A.6 (page 60). We focus on a few key variables and for ease of exposition refer to

plots of marginal effects of key variables (with solid lines indicating 95% confidence intervals)

in Figures 6-14. All coefficients in the transfer equation are presented as the average marginal

effect on the probability of transfer.11

5.1 Parent leading: Setting a ‘fixed’ transfer level

The coefficients and standard errors for key variables in the parent-leading Stackelberg model are

presented in Tables 4 (boys) and 5 (girls). The estimates for each wave are presented separately.

The first column in each case shows the average marginal effects on the probability of the child

receiving transfers. The second and third columns in each case showing tobit coefficients for

effects on the child’s labour supply assuming first exogeneity (“tobit”) then endogeneity (“FIML

2nd stg”) of labour supply to the parent’s transfer decision. We first discuss results showing

that our model is statistically identified, then show that child labour supply responds to labour

demand conditions in the expected direction, before showing how parents’ responses to these

labour demand conditions means we can reject the parent-leading Stackelberg model.

11Any comparison between sexes is not ‘other things equal’, because of systematic differences in characteristicsbetween these groups. Girls have higher prior educational performance and a lower incidence of special educationalneeds than boys, for example. The results should be interpreted as comparing average marginal effects based ona sample representative of the population of the group and time of interest.

22

Tab

le4:

Estim

ationresults:

Stackelbergmodel

withparentlead

ing(setting‘fixed

’tran

sfer

levelin

advance).

Boy

s

Wave1(age

13-14)

Wave2(age

14-15)

Wave3(age15-16)

Transfer

Work

Hou

rsWork

Hours

Transfer

Work

Hours

WorkHou

rsTransfer

WorkHou

rsWorkHou

rs(F

IML1ststg)

(tobit)

(FIM

L2ndstg)

(FIM

L1st

stg)

(tob

it)

(FIM

L2n

dstg)

(FIM

L1ststg)

(tob

it)

(FIM

L2n

dstg)

Transfer

.-2.890**

*-0.540

.-3.752***

-7.658

**.

-5.074

***

-15.16

8***

.(0.353

)(2.418)

.(0.362)

(3.462

).

(0.408

)(1.869

)

‘Perman

ent’

income

0.11

9**

*.

.0.133***

..

0.06

9*.

.percentile

(0.035)

..

(0.039)

..

(0.040

).

.

IMD

(standardized

)0.008

-0.845*

**

-0.845***

0.014

-0.987***

-0.931

***

0.02

7**

-1.111

***

-0.895

***

(0.011

)(0.209)

(0.211)

(0.010)

(0.262)

(0.271

)(0.010

)(0.303

)(0.327

)

Birth

mon

th-0.000

-0.076

-0.062

0.004*

-0.032

-0.014

0.00

3-0.317

***

-0.287

***

(0.002

)(0.052)

(0.052)

(0.002)

(0.054)

(0.054

)(0.003

)(0.086

)(0.091

)

LEA

age16

-64

0.01

9**

-0.117

-0.167

0.025**

-0.440**

-0.341

*0.02

8***

-0.778

***

-0.502

**unem

ploymentrate

(0.008)

(0.183)

(0.185)

(0.008)

(0.193)

(0.200

)(0.008

)(0.206

)(0.224

)

Priored

ucation

alperform

ance

KS3(age14

)pointscore

..

.-0.003

-0.015

-0.007

-0.001

-0.130

-0.107

(standardized

).

..

(0.007)

(0.232)

(0.235

)(0.008

)(0.268

)(0.280

)

KS2(age11

)pointscore

0.00

30.27

60.261

..

..

..

(standardized

)(0.028

)(0.186

)(0.185)

..

..

..

Parents’ed

ucation

Degree

-0.001

-0.558

-0.626

0.049

-1.642**

-1.416

0.02

6-0.910

-0.594

(0.028

)(0.689)

(0.695)

(0.031)

(0.823)

(0.867

)(0.031

)(0.933

)(0.986

)

A-Levels

-0.008

0.153

0.153

0.028

-0.227

-0.069

0.00

30.04

50.22

4(0.025

)(0.587)

(0.588)

(0.026)

(0.727)

(0.742

)(0.027

)(0.813

)(0.859

)

GCSEs

-0.012

0.106

0.137

0.027

-0.059

0.15

6-0.019

0.74

80.61

5(0.023

)(0.574)

(0.575)

(0.024)

(0.730)

(0.740

)(0.025

)(0.845

)(0.876

)

Jointsign

ificance

oflabou

rmarketvariab

les:χ2 3

14.16

8.64

26.33

24.17

11.28

22.53

38.73

18.47

29.67

(p-value)

(0.002

7)(0.000

0)

(0.0000)

(0.0000)

(0.0000)

(0.000

1)(0.000

0)(0.000

0)(0.000

0)

Observations

4868

4868

4868

Notes:Jointsignifi

cancestatisticsand

p-valu

esare

Wald

test

statistics.

Coeffi

cients

intransfercolu

mn

pre

sente

dasavera

gem

arg

inaleffects

on

thepro

bability

ofa

positivetransferbein

gm

ade(a

spre

sente

din

accom

panyin

ggra

phs).Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.*:p<

0.1;**:p<

0.05;***:p<

0.01.In

dex

ofmultip

ledeprivation

isstandard

ized

by

substra

ctingth

em

ean

and

divid

ingby

standard

deviation.M

onth

-of-birth

within

academ

icyear:

Sept(o

ldest

inyear)

=1,Aug(y

oungest

inyear)

=12.Prioreducationalperform

anceis

standard

ized

avera

gepointsc

ore

atage11

(Key

Sta

ge2)in

wave1,and

age14

(Key

Sta

ge3)in

waves2

and

3.A

dditio

nalcontrols:Pare

nt’sso

cio-econom

icstatu

s,pare

nts’em

ploym

ent,

child’s

prioreducationalperform

ance,re

sidentand

non-resident

siblings,

lone

pare

ntfam

ily,step

fam

ily,pare

nt’sillhealth

lim

itsactivities,

house

hold

own’s

hom

e(m

org

age

oroutright),child’s

specialeducationalneeds(S

EN)classifi

cation,urb

an-rura

lclassifi

cation,child’s

eth

nicity,tim

ing

ofinte

rview.

23

Tab

le5:

Estim

ationresults:

Stackelbergmodel

withparentlead

ing(setting‘fixed

’tran

sfer

levelin

advance):

Girls

Wave1(age

13-14)

Wave2(age

14-15)

Wave3(age15-16)

Transfer

Work

Hou

rsWork

Hours

Transfer

Work

Hours

WorkHou

rsTransfer

WorkHou

rsWorkHou

rs(F

IML1ststg)

(tobit)

(FIM

L2ndstg)

(FIM

L1st

stg)

(tob

it)

(FIM

L2n

dstg)

(FIM

L1ststg)

(tob

it)

(FIM

L2n

dstg)

Transfer

.-0.238**

*7.034**

.-2.796***

-10.64

9***

.-4.549

***

-11.52

1**

.(0.377

)(2.974)

.(0.346)

(1.915

).

(0.393

)(4.514

)

‘Perman

ent’

income

0.082

**

..

0.118***

..

0.10

9**

..

percentile

(0.037)

..

(0.038)

..

(0.047

).

.

IMD

(standardized

)0.01

6*-0.785**

*-0.981***

0.008

-0.337

-0.345

0.02

7**

-0.477

*-0.360

(0.009

)(0.235)

(0.280)

(0.010)

(0.252)

(0.267

)(0.001

1)(0.304

)(0.320

)

Birth

mon

th0.00

2-0.118*

*-0.146**

-0.002

-0.082

-0.103

*0.00

8***

-0.351

***

-0.298

***

(0.002

)(0.063)

(0.070)

(0.002)

(0.051)

(0.054

)(0.003

)(0.080

)(0.084

)

LEA

age16

-64

0.00

5-0.487*

*-0.549**

0.021**

-0.798***

-0.714

***

0.02

7***

-0.902

***

-0.761

***

unem

ploymentrate

(0.007)

(0.203)

(0.234)

(0.009)

(0.212)

(0.232

)(0.008

)(0.220

)(0.252

)

Priored

ucation

alperform

ance

KS3(age14

)pointscore

..

.0.000

0.711

***

0.70

6***

0.00

40.49

9**

0.54

3**

(standardized

).

..

(0.031)

(0.214)

(0.226

)(0.009

)(0.250

)(0.255

)

KS2(age11

)pointscore

-0.006

0.53

4***

0.606***

..

..

..

(standardized

)(0.009

)(0.199

)(0.220)

..

..

..

Parents’ed

ucation

Degree

-0.005

0.26

70.244

0.046

1.744*

2.04

9**

0.07

8**

1.94

8**

2.48

4***

(0.030

)(0.798)

(0.899)

(0.030)

(0.7783)

(0.833

)(0.031

)(0.899

)(0.961

)

A-Levels

-0.43*

-0.290

0.208

-0.003

1.965

***

2.01

1***

0.00

32.29

4***

2.42

1***

(0.025

)(0.694)

(0.803)

(0.026)

(0.723)

(0.757

)(0.025

)(0.791

)(0.816

)

GCSEs

-0.048*

*0.158

0.780

-0.022

2.208

***

2.01

5***

-0.002

2.65

5***

2.61

1***

(0.023

)(0.672)

(0.815)

(0.025)

(0.698)

(0.730

)(0.025

)(0.776

)(0.801

)

Jointsign

ificance

oflabou

rmarketvariab

les:χ2 3

6.81

12.13

29.12

10.48

10.24

22.80

39.57

18.29

24.10

(p-value)

(0.078

2)(0.000

0)

(0.0000)

(0.0149)

(0.0000)

(0.000

0)(0.000

0)(0.000

0)(0.000

0)

Observations

4857

4857

4857

Notes:Jointsignifi

cancestatisticsand

p-valu

esare

Wald

test

statistics.

Coeffi

cients

intransfercolu

mn

pre

sente

dasavera

gem

arg

inaleffects

on

thepro

bability

ofa

positivetransferbein

gm

ade(a

spre

sente

din

accom

panyin

ggra

phs).Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.*:p<

0.1;**:p<

0.05;***:p<

0.01.In

dex

ofmultip

ledeprivation

isstandard

ized

by

substra

ctingth

em

ean

and

divid

ingby

standard

deviation.M

onth

-of-birth

within

academ

icyear:

Sept(o

ldest

inyear)

=1,Aug(y

oungest

inyear)


anceis

standard

ized

avera

gepointsc

ore

atage11

(Key

Sta

ge2)in

wave1,and

age14

(Key

Sta

ge3)in

waves2

and

3.A

dditio

nalcontrols:Pare

nt’sso

cio-econom

icstatu

s,pare

nts’em

ploym

ent,

child’s


ance,re

sidentand

non-resident

siblings,

lone

pare

ntfam

ily,step

fam

ily,pare

nt’sillhealth

lim

itsactivities,

house

hold

own’s

hom

e(m

org

age

oroutright),child’s


EN)classifi

cation,urb

an-rura

lclassifi

cation,child’s

eth

nicity,tim

ing

ofinte

rview.

24

5.1.1 Identification

The second-stage coefficients representing the child’s labour supply response to parental trans-

fers are identified by the exclusion of parental income from the child’s labour supply equation,

and the probability of positive transfers strictly increasing in parental income. The second line

of coefficients in Tables 4 and 5 (girls)Tables shows that the latter condition clearly holds. A

10 percentile move up the income distribution increases the probability of positive transfer by

around 1 percentage point. This is statistically significant at the 5% level in five out of the six

cases and at the 10% level in the last (boys in wave 3).

5.1.2 Labour demand and child part-time work

Figure 3 shows that being born later in the academic year produces a significant employment

penalty for both boys and girls in wave 3. While the coefficients are negative for earlier waves,

they are not statistically significant. This is consistent with ‘turning 16’ specifically bringing the

significant advantage in accessing the types of jobs systematically vacated by students departing

for university. Figures 4 and 5 show that the IMD and adult unemployment rate always have

a negative effect on predicted working hours. At least one of these coefficients is statistically

significant at the 5% level in all six specifications, and when the wave 1, wave 2 and wave

3 regression models are estimated simultaneously for each gender as ‘Seemingly Unrelated’

systems, the coefficients on both IMD and the unemployment rate are jointly significantly

different from zero for both genders with p < 0.005 in all cases.

5.1.3 Testing the predictions of the Parent-leading Stackelberg model

Inspecting both the child responses to parental transfers, and how parental transfers respond

to labour demand conditions, our results are contrary to the predictions of the parent-leading

Stackelberg model in two ways.

Firstly, Figure 6 shows that boys always reduce their working hours parental transfers increase,

and this effect becomes larger as they become older. Girls also reduce their labour supply in

response to parental transfers at both ages 15 and 16. Indeed, the effect is large enough that, on

average, making transfers would crowd out all the teenager’s working hours. However, labour

supply is increasing in transfer receipt for girls in wave 1. This coefficient has a p-value of

25

Figure 3: Parent-leading Stackelberg

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2


Wave 1 Wave 2 Wave 3

Effect of being born one month later on predicted

hours of employment


-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4



Effect of one standard deviation increase in IMD on

predicted hours of employment


��

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

26

0.018 for a two-sided test. Accounting for testing for significant effects on multiple outcomes

for each individual (i.e. their labour supply at each of three points in time), this result remains

significant at the 10% level with a p-value of 0.065.12

It is possible that if girls’ employment in this age-group largely consists of babysitting younger

siblings, payment for this work may be conflated with transfers. We re-estimated the model for

children with no younger siblings (for whom there should be no within-household babysitting

work), and obtained a still positive, but much smaller and statistically insignificant coefficient,

lending limited support to this hypothesis. We present these results and discuss the broader issue

of distinguishing household and market work and present these results in full in Appendix A.5.

The second and most important empirical finding at odds with the predictions of the parent-

leading Stackelberg model is that parents are shown to increase their probability of making cash

transfers in response to the factors which restrict the child’s labour market opportunities. As

we discussed in section 2.4, the parent-leading Stackelberg model would predict that transfers

are held constant or reduced in response to such factors.


-25

-20

-15

-10

-5

0

5

10

15



Effect of receiving cash transfer on predicted hours

of employment

Figure 7 shows that parents never significantly reduce their probability of transfer for offspring

who are younger within their cohort, and for girls in the year they turn 16, significantly increase

the probability of transfer. (This result is robust to accounting for multiple testing of the

same hypothesis over each of the three waves, with the initial p-value of 0.0004 adjusted to

12This calculation uses the following Bonferroni Adjustment method, with the adjusted p-value calculated asfollows: padj = 1− (1−p(k))g(k) where g(k) = M1−r(.k). Here M is the number of outcomes being tested (3 eachfor boys and girls), p(k) is the unadjusted p-value for the kth outcome and r(.k) is the mean of the (absolute)pairwise correlations between all the outcomes other than k (i.e. the correlation between girls’ labour supply inwave 2 and wave 3, which is 0.434). See Sankoh, Huque and Duby (1997), pp.2534-2535 for discussion and Akeret al. (2011) for an economics application.

27


-0.01

-0.005

0

0.005

0.01

0.015



Average marginal effect of being one month

younger on probability of transfer


-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06



Average marginal effect of one standard deviation

increase in IMD on probability of transfer


��

��

��

��

��

��

��

��

�

��

��

��

��

��

28

0.0018).13 We cannot infer whether the absence of a corresponding effect for boys, for whom

the employment penalty is equally large, is due to systematically different treatment - parents

acting more altruistically, in terms of insuring their consumption, towards their daughters than

sons - or statistical imprecision.

In addition, Figures 8 and 9 show that the local Index of Multiple Deprivation and unemploy-

ment rate always have a positive effect on the probability of transfer. Both are statistically

significant for wave 3, and the unemployment rate coefficient is statistically significant at the

5% level in all other cases except for girls in wave 1. The average marginal effects across the

waves are jointly significantly different from zero for the unemployment rate for both genders

(boys, p = 0.002; girls, p = 0.003), and significant for the IMD for boys (p = 0.035) though

marginally insignificant for girls (p = 0.072).14

These findings show that parents’ behaviour is not time-consistent and not opportunistic in

relation to a ceiling on the child’s hours of employment. We therefore reject a parent-leading

Stackelberg model for the determination of child’s labour supply. This may mean that the

difficulty for the child to obtain and keep a job presents too often and heavy a challenge to

time-consistent behaviour by the parent. Alternatively, the parent may give too low a weight

to his own consumption relative to elements of the child’s utility, and to child’s consumption

relative to human capital, for this decision-making process to make him best off. Either way,

it seems parents prefer to ‘insure’ their child’s consumption against labour market difficulties

outside their control (Ermisch, 2003, p.5).

5.2 Child leading, or parent setting a contingent transfer schedule

We now present results for the child-leading Stackelberg framework, in which shifts in the

child’s labour supply decision identify the parent’s best-response correspondence. Coefficients

and standard errors for key variables are presented in Tables 6 (boys) and 7 (girls), and again

the estimates for each wave are presented separately. The first column in each case shows tobit

coefficients for the effect on the child’s labour supply. The second and third columns in each

case show average marginal effects on the probability of the child receiving transfers assuming

13Using the same Bonferroni Adjustment method as described in footnote 13, with M = 3 and r(.k) = 0.314314These findings show that the IMD is not acting as a proxy for unobserved household level characteristics

with which it is correlated. If this were the case, one would expect a negative sign, because generally the moreaffluent the household, and hence the greater the probability of the transfer, the lower the IMD. As such, we areconfident that by including household level counterparts to the deprivation indicators captured by the IMD, thecoefficients here represent the contextual effect of local labour market conditions.

29

first exogeneity (“probit”) then endogeneity (“FIML 2nd stg”) of transfers to the child’s labour

supply decision. Again, we first present results showing that our model is statistically identified,

before showing how parents’ best response correspondence is a function of household income

and the child’s labour supply.

5.2.1 First stage: Labour supply equation

The parent’s best response correspondence is identified by changes in the child’s labour supply

driven by labour demand factors which we assume have no direct effect on parental transfers,

conditional on the household and area characteristics for which we also control. Figures 10-12,

and the third, fourth and fifth lines of coefficients in Tables 6 and 7 show that the unemployment

rate, IMD and month of birth on labour supply all have the expected negative effect on child

labour supply. Within each gender and wave, they are always jointly significant at the the 5%

level or less. These graphs also support the decision to estimate seperately by wave and sex.

Both boys and girls become progressively more responsive to the adult unemployment rate as

they get older. While the difference in coefficients is not statistically significant, boys appear

better insulated from this wider adult labour market, instead (at least at ages 15 and 16) being

dependent on very localised determinants of opportunities, proxied by the IMD. Turning 16 (in

wave 3) earlier than one’s peers is the only birthday that matters significantly for employment

opportunities. This suggests that jobs this birthday opens up; involving alcohol or catering;

are more common among vacancies created by 18 year-olds leaving for university than those for

which the lifting of the 5-hour Saturday restriction (on one’s 15th birthday) would be employers’

binding concern.

30

Tab

le6:

Estim

ationresults:

Stackelbergmodel

withchildlead

ing,

orparentsettingcontingenttransfer

sched

ule:Boys

Wave1(age

13-14)

Wave2(age

14-15)

Wave3(age15-16)

WorkHours

Transfer

Transfer

WorkHou

rsTransfer

Transfer

Work

Hours

Transfer

Transfer

(FIM

L1ststg)

(probit)

(FIM

L2n

dstg)

(FIM

L1ststg)

(probit)

(FIM

L2ndstg)

(FIM

L1st)

(probit)

(FIM

L2ndstg)

Work

Hou

rs.

-0.019

***

-0.005

.-0.020**

*-0.010*

.-0.019***

-0.007

.(0.002

)(0.006

).

(0.002

)(0.005)

.(0.002)

(0.004)

‘Permanant’

income

0.391

0.10

3**

*0.10

1***

-1.389

0.096*

*0.101**

-0.319

0.059

0.055

percentile

(0.909)

(0.036

)(0.036

)(1.014

)(0.039

)(0.040)

(1.277)

(0.038)

(0.039)

IMD

(standardized

)-0.817*

**.

.-1.017

***

..

-1.158***

..

(0.207

).

.(0.267

).

.(0.317)

..

Birth

month

-0.064

..

-0.037

..

-0.326***

..

(0.052

).

.(0.053

).

.(0.088)

..

LEA

age

16-64

-0.125

..

-0.489

**.

.-0.818***

..

unem

ploymentrate

(0.184

).

.(0.202

).

.(0.222)

..

Prioreducationalperf’

KS3(age14

)point

..

.0.02

3-0.006

-0.006

-0.102

-0.007

-0.006

score

(standardized)

..

.(0.234

)(0.008

)(0.008)

(0.274)

(0.009)

(0.009)

KS2(age11

)point

0.251

0.00

50.00

4.

..

..

.score

(standardized)

(0.186

)(0.008)

(0.008

).

..

..

.

Parents’education

Degree

-0.652

-0.011

-0.016

-1.723

**0.02

30.029

-1.062

0.003

0.006

(0.707

)(0.029)

(0.028

)(0.863

)(0.029

)(0.031)

(0.971)

(0.030)

(0.031)

A-Levels

0.158

-0.014

-0.018

-0.230

0.01

30.014

0.088

-0.008

-0.010

(0.590

)(0.025)

(0.025

)(0.753

)(0.025

)(0.026)

(0.837)

(0.027)

(0.027)

GCSEs

0.165

-0.016

-0.073

-0.018

0.01

70.017

0.870

-0.019

-0.024

(0.572

)(0.024)

(0.024

)(0.745

)(0.023

)(0.024)

(0.864)

(0.025)

(0.004)

Jointsign

ificance

oflabourmarketvariables:

24.49

..

34.85

..

47.94

..

χ2 3(p-value)

(0.000

0)

..

(0.000

0).

.(0.0000)

..

Observation

s48

6848

684868

Notes:Jointsignifi

cancestatisticsand

p-valu

esare

Wald

test

statistics.

Estim

ating

all

six

specifi

cationsjointly

obta

insW

ald

test

statistic

ofχ2 6

=23.64

(p=0.0006)forjointsignifi

canceofchildre

n’s

Work

Hours

on

pare

nts’pro

bability

oftransfer.

Coeffi

cients

intransfercolu

mn

pre

sente

dasavera

ge

marg

inaleffects

on

the

pro

bability

ofa

positive

transferbein

gm

ade

(aspre

sente

din

accom

panyin

ggra

phs).

Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.*:p

<0.1;**:p

<0.05;***:p

<0.01.In

dex

ofmultip

ledeprivation

isstandard

ized

by

substra

cting

them

ean

and

divid

ing

by

standard

deviation.M

onth

-of-birth

within

academ

icyear:

Sept(o

ldest

inyear)

=1,Aug

(youngest

inyear)


anceis

standard

ized

avera

gepointsc

ore

atage11

(Key

Sta

ge2)in

wave1,and

age14

(Key

Sta

ge3)in

waves2

and

3.A

dditio

nalcontrols:Pare

nt’sso

cio-econom

icstatu

s,pare

nts’em

ploym

ent,

child’s


ance,re

sidentand

non-residentsiblings,

lonepare

ntfam

ily,

step

fam

ily,pare

nt’sillhealth

lim

itsactivities,

house

hold

own’s

hom

e(m

org

ageoroutright),child’s


EN)classifi

cation,urb

an-rura

lclassifi

cation,child’s

eth

nicity,tim

ing

ofinte

rview.

31

Tab

le7:

Estim

ationresults:

Stackelbergmodel

withchildlead

ing,

orparentsettingcontingenttransfer

sched

ule:Girls

Wave1(age13-14)

Wave2(age

14-15)

Wave3(age

15-16)

WorkHou

rsTransfer

Transfer

WorkHou

rsTransfer

Transfer

WorkHou

rsTransfer

Transfer

(FIM

L1ststg)

(probit)

(FIM

L2n

dstg)

(FIM

L1ststg)

(probit)

(FIM

L2n

dstg)

(FIM

L1ststg)

(probit)

(FIM

L2n

dstg)

WorkHou

rs.

-0.016

***

-0.002

.-0.016

***

-0.009

.-0.019

***

-0.015

***

.(0.003

)(0.007

).

(0.002

)(0.006

).

(0.001

)(0.004

)

‘Perman

ant’

income

-0.094

0.087

**0.08

6**

-1.726

*0.09

5**

0.09

8**

-0.572

0.08

7**

0.08

9**

percentile

(0.986

)(0.038

)(0.039

)(1.010

)(0.038

)(0.039

)(1.190

)(0.040

)(0.040

)

IMD

(standardized

)-0.808

***

..

-0.399

..

-0.577

*.

.(0.238)

..

(0.258

).

.(0.320

).

.

Birth

mon

th-0.121

*.

.-0.085

*.

.-0.393

***

..

(0.064)

..

(0.051

).

.(0.083

).

.

LEA

age16

-64

-0.482

**.

.-0.869

***

..

-1.031

***

..

unem

ploymentrate

(0.202

).

.(0.221

).

.(0.233

).

.

Prior

education

alperf’

KS3(age

14)point

..

.0.72

0***

0.00

20.00

20.48

6*0.00

10.00

1score(standardized

).

..

(0.214

)(0.009

)(0.009

)(0.258

)(0.008

)(0.009

)

KS2(age

11)point

0.55

0***

-0.006

-0.007

..

..

..

score(standardized

)(0.201

)(0.009

)(0.009

).

..

..

Parents’ed

ucation

Degree

0.25

3-0.013

-0.014

1.67

5**

0.04

10.04

11.51

00.06

8**

0.07

3**

(0.810)

(0.031

)(0.030

)(0.796

)(0.028

)(0.031

)(0.935

)(0.026

)(0.031

)

A-Levels

-0.190

-0.049

*-0.049

**2.06

5***

-0.002

-0.006

2.30

2***

0.00

70.00

5(0.695)

(0.026

)(0.023

)(0.735

)(0.026

)(0.026

)(0.814

)(0.025

)(0.025

)

GCSEs

0.29

5-0.050

**-0.050

**2.26

8***

-0.018

-0.022

2.65

2***

0.00

2-0.001

(0.676)

(0.024

)(0.023

)(0.706

)(0.025

)(0.025

)(0.798

)(0.002

)(0.025

)

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Notes:Jointsignifi

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32

Figure 10: Child-leading Stackelberg

��

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��


-2

-1.5

-1

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Effect of one standard deviation increase in IMD on

predicted hours of employment


-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1



Effect of being born one month later on predicted

hours of employment

33

5.2.2 Second stage: Parent’s transfer or tax schedule

Figure 13 shows that parent’s transfer probability is always increasing in household income. The

effect is small, akin to a 10 percentage point movement up the income distribution increasing the

probability of transfers by approximately 1 percentage point. We expected a small magnitude for

the income gradient. Earlier work by Dustmann et al. (2009) and Dustmann and Micklewright

(2001) identified a marginal propensity for parents to transfer income to their children of just

0.005 on average, for example. With transfers somewhat inelastic with respect to parental

income, this is consistent with Dustmann et al’s (1996) argument that youths from lower-income

households do not face “disproportionately high financial pressure” to work.15

Figure 14 shows that transfer probability is always decreasing in hours of employment, but this

effect is statistically significant only for girls in wave 3, which is the final year of compulsory

education. This result is robust to adjusting for our testing of multiple null hypotheses (in this

case, that the coefficient on hours of work is zero in each of three time periods). The initial

p-value of 0.0012 becomes 0.0041 after making this adjustment.16 As such, for this final group,

we can firmly reject the null hypothesis that parents do not tax their children. More generally,

when wave 1, wave 2 and wave 3 regression models for each gender are estimated simultaneously

as ‘Seemingly Unrelated’ systems, these ‘tax rate’ coefficients across all three waves are jointly

significantly less than zero at the 1% level for girls (p=0.0038) but and 10% level for boys

(p=0.0563).

These conclusions are clearly affected by the fact that we have information on the extensive

margin only (i.e. whether there is a transfer from parents to children or not). There could be

adjustments on the intensive margin (the amount), but as these changes are not observable our

statistical power to detect parents’ behavioural responses is limited. Our estimates here tell us

simply that the ‘tax rate’ at the intensive margin is sufficiently shallow to mean that increasing

labour supply results in very few cases of parents switching from positive to zero transfers.

Parents are sufficiently altruistic and paternalistic to adopt this decision-making mechanism

in preference to setting a ‘fixed’ transfer level, but since they are not observed to discourage

employment through a heavy ‘tax rate’, these results imply they do not perceive having a job

15A potential alternative strategy was to identify the effect of income changes over time on transfers. Thisproved infeasible due to the differences in income measurement between waves.

16Here we use the same Bonferroni Adjustment method described in footnote 13. The number of outcomesbeing tested is again 3, and r(.k), the mean of the (absolute) pairwise correlations between all the outcomes otherthan k (i.e. the correlation between girls’ cash transfer receipt in wave 1 and wave 2) is 0.452

34

to be particularly damaging to the child’s human capital or educational performance.


-0.05

0

0.05

0.1

0.15

0.2



Average marginal effect of relative permanent

income on probability of cash transfer


-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015



Ave' marginal effect one hour p.week increase in

child employment on prob' of cash transfer

Nevertheless, we might expect the productivity of study time, in terms of educational perfor-

mance measured at the end of school year 11, to be highest in that final year of compulsory

schooling; and the amount of study time undertaken also to be highest close to these final ex-

ams, resulting in the greatest scope for study time being crowded out. Certainly, it has been

shown that the net effect of in-school employment is more detrimental to academic performance

in closer proximity to examinations (Ruhm, 1997; Payne, 2004). In this case, we would expect

parents’ incentive to use their financial resources to deter in-school employment, and hence our

ability to detect such a tax schedule, to be highest in the final year of compulsory education.

The results in Figure 14 are consistent with this prediction, though also imply that, at least for

work undertaken during this final year, parents perceive the net effect of in-school labour supply

35

to be more detrimental for girls than boys.17 This may be because girls dominate employment

in ‘child-oriented’ roles such as babysitting (Kooreman, 2009), which may contribute more to

family-oriented and less to career-oriented skills and preferences, resulting in less favourable

long-run labour market outcomes due to changes in fertility decisions, for example (Erdogan

et al., 2012). An alternative explanation is that parents have a higher relative preference for

education-oriented human capital in their daughters than sons, perhaps reflecting women’s

higher wage returns to educational qualifications (Machin, 2005; Bonesrønning, 2010).18

6 Conclusion

Employment experience for teenagers in compulsory education has a potentially significant

impact on educational performance and subsequent academic and labour market opportunities.

This paper has focused on the idea that parents can use financial incentives to alter their child’s

decision to work, and developed a theoretical model for the interaction determining the financial

support provided by parents and part-time employment taken by children. We motivate two

alternative Stackelberg frameworks. In the first (parent-leading), parents set their transfer level

in advance, anticipating the child’s best-response. In the second (child leading) parents set a

contingent transfer schedule for each level of labour supply, effectively taxing their children’s

earnings.

We test our model using data on a cohort of English teenagers between 2004 and 2006, estimat-

ing cross-sectional models for the same sample of individuals at ages 14, 15, and 16. Holding

constant the institutional arrangements, education system and time-invariant unobserved char-

acteristics, we identify significant differences in the determinants of selection into employment

17The results in Holford (2016), estimated using the same cohort of individuals, suggest that such an expectationwould be rational. Most previous literature either focuses exclusively on males, in order that longer-run labourmarket outcomes may be considered without fertility considerations, or does not allow for heterogeneous effectsby gender. The extant evidence is inconclusive. Ruhm (1997) suggests the human capital benefit of in-schoolemployment is greater for females but D’Amico (1984) shows the opposite conclusion, while Rothstein (2007)shows similar and small negative effects for both genders.

18In this approach, we have implicitly assumed the same decision-making process is adopted by all households.However, as we note in section 2.3, the less paternalistic and more selfish is the parent, the more likely it is thatshe will prefer to set a fixed transfer level. Heterogeneous preferences may therefore lead to heterogeneity in thedecision-making mechanism. Recognizing this, strictly speaking, our results show only that a sufficiently largeproportion of parents adopt the child-leading model that the parent-leading model can be rejected in statisticalterms. In Appendix A.1 (page 44), we derive the predictions of the model assuming the parent gains no utilityfrom human capital, and show estimates for two subpopulations of potential policy interest: households in whichthe parent (i) would like the child to leave full-time education at the minimum age and (ii) has no qualifications.Though hampered by small samples, these estimates provide tentative evidence for these households moving fromthe parent-leading to child-leading mechanism between ages 14 and 16.

36

as the children age, but do not detect significant differences in the propensity of parents to ‘tax’

their children’s earnings over this time.

Estimates from the empirical counterpart to the parent-leading framework show that parents

use their relative financial power to ‘insure’ their child’s consumption against factors beyond

their control. Rather than holding transfers constant in response to factors affecting the child’s

labour market opportunities, or reducing them in response to a ceiling being placed on their

hours of employment, parents raise transfers instead. This suggests that parents would like

their children to provide for their own consumption, but will not penalize them if this proves

difficult. We also demonstrate a very shallow income gradient in parent’s willingness to make

cash transfers to the child. These results suggest that parents of children who otherwise would

leave education at 16 can and will accommodate the two additional years of schooling which,

from 2013-2014, have been becoming compulsory in the UK, as an ‘extension to childhood’,

rather than impose a financial burden on an ‘independent adult’. This should ensure the

benefits to extended compulsory education will not be hindered by financial pressures to take

employment.

These results are inconsistent with a model in which parents set a ‘fixed’ transfer level. We

therefore reject the parent-leading Stackelberg framework. The findings are in line with a

situation in which parents set a contingent transfer schedule for each possible level of the child’s

labour supply. In the language of game theory this can be interpreted as the parent - whose

financial resources afford the choice between the two decision-making mechanisms - being better

off by ceding the Stackelberg first-move advantage to the child. The child’s human capital is a

public good, valued by both the parent and the child but potentially eroded by long hours of

employment. In this framework, by taxing the child’s earnings the parent forces the child to

internalise this social cost. This cannot be achieved with a fixed lump-sum transfer.

We find that the probability of receiving transfers is always decreasing in the child’s hours of

employment, so parents do tax their children, though this is only significant for girls in the

final year of compulsory schooling. Further work should try to explore whether this gender

distinction is due to gender differences in parental perceptions of the education production

function or gender-specific parental preferences for education-oriented human capital.

Our results suggest there is little case for more restrictive regulation of in-school employment

on equity grounds. There is strong positive selection into employment by prior educational

37

performance, and the shallow income gradient in parental transfers reveals no evidence that

consumption pressures drive low socio-economic status children into employment. Nevertheless,

from the perspective of a social planner, it may still be the case that parents underestimate the

human capital cost of employment, leading to sub-optimal outcomes.

38

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43

A Appendix

A.1 Parents with no preference for human capital

The theoretical predictions in the main body of this paper are driven by the assumption that

the parent is paternalistic; she cares more about the child’s human capital than does the child

himself. This enables us to reject the Nash equilibrium on welfare grounds, and our empirical

results suggest that parents’ relative preference for human capital is sufficiently high for them to

prefer to set a contingent transfer schedule based on the child’s labour market earnings, rather

than a fixed transfer level. Thus, it is the parent’s preference for human capital that drives her

to ‘insure’ the child’s consumption against labour market factors outside the child’s control.

In this appendix, we show how the predictions of the model change when the parent does not

care about the child’s human capital. We show that in this case, in common with conventional

non-cooperative games, she will prefer to move first and set a fixed transfer level, thus no

longer insuring the child’s consumption. We test the same predictions of the parent-leading

Stackelberg model for two subpopulations that may be expected to have a lower preference

for human capital than the pooled population: parents who declare that they would like their

child to leave full-time education at age 16; and parents with no educational qualifications. We

find tentative evidence that parents in these groups transition from the parent-leading to the

child-leading model between the child’s ages of 14 and 16, suggesting either that the parent’s

relative preference for human capital, or their perception of the negative human capital effect

of in-school employment, increases over time.

A.1.1 Parent’s maximisation problem

The parent’s maximisation problem under a Nash equilibrium or when she acts as a Stackelberg

follower, in either case taking the child’s action as given, is now as follows:

maxt

Up = Up(P (M − t), C(wL+ t), κp(X)) (A1)

Because in these cases, she takes the child’s action (L) as given, her optimality condition is

unchanged:

UpC = U

pP (A2)

44

Acting as a Stackelberg leader, the parent must account for the indirect effects of t on the utility

from consumption, but no longer from the child’s human capital, caused by the child’s labour

supply response to t:

maxt

Up = Up(P (M − t), C(wL∗(t) + t), κp(X)) (A3)

The parent’s optimality condition as a Stackelberg leader is, hence:

UpC(1 +

∂L∗

∂t· w) = U

pP (A4)

Since the child’s maximisation problems and optimality conditions are unchanged, he will still

reduce labour supply in response to increasing transfers, so ∂L∗

∂t< 0. This means, at the Nash

equilibrium level of transfers it holds that:

UpC(1 +

∂L∗

∂t· w) < U

pP (A5)

From this position, a parent who does not care about the child’s human capital will reduce

transfers, thereby increasing her own consumption (and reducing its marginal utility UpP ) and

reducing the child’s (increasing his marginal utility U cC). This means that the parent-leading

Stackelberg equilibrium will occur at lower transfers and higher labour supply than the Nash

equilibrium.

This situation can again be represented graphically, as shown in Figure 15. There are two key

differences from the situation portrayed in Figure 1. Firstly, since the parent now will now never

subsidise employment in order to encourage human capital accumulation, there is no range of

labour supply over which the parent increases transfers in response to increased labour supply.

This means that ∂t∗

∂L< 0 for all L, not only in equilibrium, so the parent’s BR is downward

sloping over its entire range. Secondly, the parent’s bliss point is now above the child’s best-

response correspondence, meaning that the parent-leading Stackelberg model is strictly preferred

to the Nash equilibrium, in turn strictly preferred to the child-leading Stackelberg equilibrium.

The child’s preference ordering is precisely the opposite (Since the child’s optimality condition

is unchanged, the child-leading Stackelberg equilibrium will still occur at higher labour supply

and lower transfers than the Nash equilibrium).

45

Figure 15: Agents’ optimisation problem and the three equilibria when the parent has nopreference for child’s human capital

Parent bliss point

Human

cap’ max’

0 → t t

L

↑

0

L

= t*(L, M, X)

= L*(t, w, X)

Child bliss

point at

t=∞

Nash equilibrium

Child-leading

Stackelberg

equilibrium

Parent-leading

Stackelberg

equilibrium

Increasing child’s utility

Increasing parent’s utility

A.2 Estimates

Our estimates of the parent-leading model are shown in Tables A1 and A2, and the child-leading

model in Tables A3 and A4. In each case, the results for the group whose parents would like

them to leave full-time education at 16 is shown in the upper panel, those whose parents have

no qualifications in the lower panel, and in both cases boys first.

In the parent-leading model we must first note that in three cases (for sons of parents who would

like them to leave at 16, in waves 2 and 3, and daughters of parents with no qualifications, in

wave 1), the coefficient on ‘permanent’ income is negative. Though in these cases the effect

is not significant, the positive coefficients obtained in the majority of other cases also fail to

obtain significance. This means that the effect of transfers on labour supply in the second stage

of these models is not identified. Nevertheless, by focusing on the first stage results we are able

to test the prediction of the parent leading model that the parent reduces or does not alter

transfers in response to labour market difficulties faced by the child.

For the group whose parents would like them to leave full-time education, among boys we fail to

reject this hypothesis in wave 1. Indeed, there is strong evidence that parents are less likely to

46

give transfers to children who are younger within the school year (having controlled for month

of interview, including a dummy for interview after the child’s birthday). In wave 2, we again

fail to reject the hypothesis, but in wave 3, it is firmly rejected due the statistically significant

positive coefficient on the LAD unemployment rate.

For girls, in wave 1 we find a positive coefficient on IMD, which is significant at the 5% level, but

conversely, a negative coefficient on the cusp of significance at the 10% level, for the unemploy-

ment rate, though it should also be noted that for this sample, the effect of this unemployment

rate on hours of employment is positive but not statistically different from zero. This suggests

tentative grounds to reject the parent-leading model, but in wave 2 there is no such evidence. In

wave 3, the coefficients on IMD, birth month and unemployment are all positive, with the coef-

ficient on birth month individually and the three coefficients jointly significant at the 10% level,

meaning that there are again grounds to reject the parent-leading model. (Note the especially

small sample for this specification, with which a 10% rejection is relatively more acceptable).

For those whose parents have no qualifications the picture is simpler. For boys the parent-

leading model cannot be rejected in wave 1, there are grounds for rejection in wave 2 (a 5%

significant positive coefficient on unemployment, though the three variables together are not

collectively significant), and a firmer rejection in wave 3, due to the 1% significant coefficient

on IMD. For girls, we always reject the parent-leading model, firmly in waves 1 and 3, less so

in wave 2, where the coefficient on birth month is in fact negative (with a t-statistic of 1), but

on the other two is positive and on the cusp of significance).

Moving to the child-leading model, the counterpart testable prediction is that we should obtain

a negative coefficient on Work Hours in the parent’s transfer equation. The failure to obtain

statistical significance in the main body of the paper with the larger sample suggests obtaining

robust inference on this hypothesis is challenging.

Nevertheless, at face value, we observe a positive (though never signifcant at any level) coefficient

on Work Hours in the Transfer equation in three cases, all for girls; in waves 1 and 2 among those

whose parents wanted them to leave education, and in wave 1 among those whose parents have

no qualifications. In the former two cases, we failed to reject the parent-leading model, while

in the last the parent leading model was rejected somewhat strongly. We observe a negative

coefficient at the 5% level only for girls whose parents want them to leave, in wave 3 of the

survey, which is consistent with the results in the main body of this paper.

47

Altogether, therefore, the results presented in this section show that, even if parents’ stated

attitude places a low weight on educational human capital (since they would prefer their child

to leave full-time education as soon as possible), by the time the child reaches the final year of

compulsory schooling their observed behaviour is sufficient to reject the parent-leading model

and consistent with setting a contingent transfer level, or ‘taxing’ their children. This means

that despite their stated preference, they still care sufficiently about the effects of labour supply

on immediate educational performance to prefer this strategy over setting a ‘fixed’ transfer

level. However, there is some tentative evidence that, unlike the general population, while the

children are aged 14 or 15, parents may prefer to set a fixed transfer level.

Our interpretation of this finding is that, at age 14, this subpopulation cares less about human

capital than the general population, but this preference increases over time as the importance

of educational qualifications for early labour market opportunities becomes more salient.

48

Table A1: Estimation results for subpopulation of parents who would like child to leave full-timeeducation at age 16: Parent-leading model

Boys

Wave 1 (age 14) Wave 2 (age 15) Wave 3 (age 16)

Transfer Work Hours Transfer Work Hours Transfer Work Hours(1st stg) (2nd stg) (1st stg) (2nd stg) (1st stg) (2nd stg)

Transfer . -6.375 . -10.249 . -15.917. (4.259) . (10.034) . (5.685)

‘Permanent’ income 0.110 . -0.228 . -0.121 .percentile (0.076) . (0.082) . (0.076) .

IMD (standardized) -0.004 -0.613 0.021 -0.961* 0.011 0.186(0.019) (0.416) (0.021) (0.536) (0.022) (0.659)

Birth month -0.017*** -0.101 0.005 -0.047 -0.009 -0.587***(0.005) (0.134) (0.005) (0.139) (0.006) (0.218)

LAD age 16-64 0.022 0.141 0.016 -0.246 0.056*** -0.968unemployment rate (0.017) (0.367) (0.016) (0.465) (0.019) (0.619)

Joint significance of labour 13.20 2.74 4.55 4.90 15.94 9.61market variables: χ2

3(p-value) (0.004) (0.433) (0.208) (0.179) (0.001) (0.022)

Observations 981 1077 1034

Girls



Transfer . 2.297 . -19.712*** . -10.103. (9.038) . (3.204) . (9.606)

‘Permanent’ income 0.103 . 0.020 . -0.151 .percentile (0.139) . (0.083) . (0.133) .

IMD (standardized) 0.057** -0.368 0.021 0.240 0.023 -1.618*(0.024) (0.889) (0.029) (1.004) (0.036) (0.963)

Birth month 0.006 -0.256 -0.002 -0.126 0.018* -0.287(0.008) (0.205) (0.006) (0.204) (0.009) (0.302)

LAD age 16-64 -0.0451 0.297 0.037 -0.525 0.039 -0.357unemployment rate (0.027) (0.804) (0.022) (0.864) (0.027) (0.736)


3(p-value) (0.176) (0.573) (0.168) (0.868) (0.059) (0.205)


Notes: 1: p-value = 0.101. So on margin of statistical significance. Joint significance statistics and p-values are Wald test statistics. Coefficientsin transfer column presented as average marginal effects on the probability of a positive transfer being made. Standard errors, clustered byschool, in parentheses. Longitudinal weights applied. *: p ≤ 0.1; **: p ≤ 0.05; ***: p ≤ 0.01. Index of multiple deprivation is standardizedby substracting the mean and dividing by standard deviation. Month-of-birth within academic year: Sept (oldest in year) = 1, Aug (youngestin year) = 12. Prior educational performance is standardized average point score at age 11 (Key Stage 2) in wave 1, and age 14 (Key Stage3) in waves 2 and 3. Additional controls: Parent’s highest qualification, parent’s socio-economic status, parents’ employment, child’s prioreducational performance, resident and non-resident siblings, lone parent family, child’s special educational needs (SEN) classification, urban-ruralclassification, child’s ethnicity, timing of interview.

49

Table A2: Estimation results for subpopulation of parents who have no qualifications: Parent-leading model

Boys



Transfer . 11.663 . 12.086 . -13.033. (5.097) . (17.988) . (7.684)

‘Permanent’ income 0.128 . 0.046 . 0.073 .percentile (0.081) . (0.144) . (0.120) .

IMD (standardized) 0.016 -2.358*** 0.004 -0.378 0.065*** -0.427(0.023) (0.690) (0.026) (1.267) (0.026) (1.219)

Birth month -0.002 -0.041 0.001 -0.164 -0.004 -0.622(0.006) (0.200) (0.007) (0.357) (0.008) (0.431)

LAD age 16-64 0.010 0.130 0.048** -1.950 0.034 0.079unemployment rate (0.018) (0.547) (0.024) (2.047) (0.022) (0.801)


3(p-value) (0.605) (0.006) (0.141) (0.694) (0.001) (0.374)


Girls



Transfer . -8.078 . -17.382 . 2.324. (10.599) . (11.736) . (5.555)

‘Permanent’ income -0.090 . 0.206 . 0.291** .percentile (0.110) . (0.122) . (0.126) .

IMD (standardized) 0.046** -0.892 0.044 0.105 0.093*** -1.293(0.019) (0.736) (0.025) (1.290) (0.025) (1.195)

Birth month 0.001 -0.480** -0.007 -0.053 0.015* -0.417(0.006) (0.209) (0.007) (0.364) (0.009) (0.349)

LAD age 16-64 0.016 0.503 0.034 -0.263 0.016 -1.104unemployment rate (0.016) (0.621) (0.022) (1.095) (0.021) (0.834)


3(p-value) (0.015) (0.068) (0.008) (0.993) (0.000) (0.103)


Notes: 1: p-value = 0.101. So on margin of statistical significance. Joint significance statistics and p-values are Wald test statistics. Coefficientsin transfer column presented as average marginal effects on the probability of a positive transfer being made. Standard errors, clustered byschool, in parentheses. Longitudinal weights applied. *: p ≤ 0.1; **: p ≤ 0.05; ***: p ≤ 0.01. Index of multiple deprivation is standardizedby substracting the mean and dividing by standard deviation. Month-of-birth within academic year: Sept (oldest in year) = 1, Aug (youngestin year) = 12. Prior educational performance is standardized average point score at age 11 (Key Stage 2) in wave 1, and age 14 (Key Stage3) in waves 2 and 3. Additional controls: Parent’s highest qualification, parent’s socio-economic status, parents’ employment, child’s prioreducational performance, resident and non-resident siblings, lone parent family, child’s special educational needs (SEN) classification, urban-ruralclassification, child’s ethnicity, timing of interview.

50

Table A3: Estimation results for subpopulation of parents who would like child to leave full-timeeducation at age 16:: Child-leading model

Boys



Work Hours . -0.012 . -0.011 . -0.002. (0.013) . (0.009) . (0.010)

‘Permanant’ income -0.985 0.097 0.080 -0.040 4.150* -0.097percentile (1.746) (0.077) (1.927) (0.079) (2.477) (-0.002)

IMD (standardized) -0.592 . -1.099** . 0.187 .(0.407) . (0.507) . (0.651) .

Birth month -0.008 . -0.088 . -0.476** .(0.137) . (0.124) . (0.210) .

LAD age 16-64 0.027 . -0.405 . -1.499** .unemployment rate (0.368) . (0.415) . (0.652) .

Joint significance of labour 2.57 . 10.12 . 10.18 .market variables: χ2

3(p-value) (0.463) . (0.018) . (0.017) .


Girls



Work Hours . 0.018 . 0.006 . -0.029***. (0.021) . (0.167) . (0.009)

‘Permanant’ income 4.624 0.044 1.616 0.125 6.094* -0.046percentile (2.522) (0.021) (2.833) (0.104) (3.123) (0.113)

IMD (standardized) 0.217 . -0.278 . -1.596* .(0.734) . (0.942) . (0.906) .

Birth month -0.331* . -0.116 . -0.569** .(0.184) . (0.195) . (0.259) .

LAD age 16-64 -0.085 . -0.586 . -0.875 .unemployment rate (0.732) . (0.853) . (0.707) .


3(p-value) (0.350) . (0.780) . (0.003) .


Notes: Joint significance statistics and p-values are Wald test statistics. Coefficients in transfer column presented as average marginal effectson the probability of a positive transfer being made. Standard errors, clustered by school, in parentheses. Longitudinal weights applied. *:p ≤ 0.1; **: p ≤ 0.05; ***: p ≤ 0.01. Index of multiple deprivation is standardized by substracting the mean and dividing by standard deviation.Month-of-birth within academic year: Sept (oldest in year) = 1, Aug (youngest in year) = 12. Prior educational performance is standardizedaverage point score at age 11 (Key Stage 2) in wave 1, and age 14 (Key Stage 3) in waves 2 and 3. Additional controls: Parent’s highestqualification, Parent’s socio-economic status, parents’ employment, child’s prior educational performance, resident and non-resident siblings,lone parent family, child’s special educational needs (SEN) classification, urban-rural classification, child’s ethnicity, timing of interview.

51

Table A4: Estimation results for subpopulation of parents who have no qualifications: Child-leading model

Subpopulation: Parent has no qualifications

Boys



Work Hours . -0.021 . -0.021* . -0.017. (0.173) . (0.013) . (0.013)

‘Permanant’ income 5.523** 0.062 4.234 0.053 2.526 0.062percentile (2.763) (0.100) (5.181) (0.109) (5.347) (0.114)

IMD (standardized) -1.901*** . -0.116 . -1.048 .(0.526) . (1.114) . (1.187) .

Birth month -0.082 . -0.139 . -0.556 .(0.145) . (0.314) . (0.417) .

LAD age 16-64 0.366 . -0.950 . 0.432 .unemployment rate (0.534) . (1.013) . (0.826) .


3(p-value) (0.003) . (0.639) . (0.183) .


Girls



Work Hours . 0.009 . -0.002 . -0.012. (0.021) . (0.020) . (0.021)

‘Permanant’ income 5.665* -0.090 -2.885 0.219 -0.583 0.225*percentile (2.830) (0.095) (5.134) (0.110) (5.208) (0.130)

IMD (standardized) -0.984 . -0.417 . -1.118 .(0.711) . (1.233) . (1.446) .

Birth month -0.486** . 0.033 . -0.398 .(0.197) . (0.332) . (0.357) .

LAD age 16-64 0.451 . -0.614 . -0.992 .unemployment rate (0.571) . (1.175) . (0.842) .


3(p-value) (0.039) . (0.8898) . (0.2211) .


Notes: Joint significance statistics and p-values are Wald test statistics. Coefficients in transfer column presented as average marginal effectson the probability of a positive transfer being made. Standard errors, clustered by school, in parentheses. Longitudinal weights applied. *:p ≤ 0.1; **: p ≤ 0.05; ***: p ≤ 0.01. Index of multiple deprivation is standardized by substracting the mean and dividing by standard deviation.Month-of-birth within academic year: Sept (oldest in year) = 1, Aug (youngest in year) = 12. Prior educational performance is standardizedaverage point score at age 11 (Key Stage 2) in wave 1, and age 14 (Key Stage 3) in waves 2 and 3. Additional controls: Parent’s highestqualification, Parent’s socio-economic status, parents’ employment, child’s prior educational performance, resident and non-resident siblings,lone parent family, child’s special educational needs (SEN) classification, urban-rural classification, child’s ethnicity, timing of interview.

52

A.3 Observed social interactions

This section derives the child’s labour supply response to unearned income in the Nash or

parent-leading Stackelberg models and the parent’s transfer response to child labour supply in

the Nash or child-leading Stackelberg model. These parameters are derived from the implicit

functions which are the first-order conditions in equations (4) and (9).

A.3.1 The labour supply response to unearned income

The child’s first-order condition is:

[.] = w · U cC +HL · U c

H = 0 (A6)

Using implicit differentiation, the parameter of interest is equal to:

∂L

∂t= −

[∂[.]∂t

]

[∂[.]∂L

](A7)

= −∂[wUc

C ]

∂t+

∂[UcHHL]

∂t∂[wUc

C]

∂L+

∂[UcH

HL]

∂L

The elements of this expression are as follows:

• .∂[w·Uc

C ]∂t

= wU cCC : w is constant, and increasing t by 1 increases consumption by 1.

• .∂[Uc

HHL]∂t

= 0: Human capital production function is invariant to transfers, and marginal

utility from human capital and consumption are separable.

• .∂[wUc

C ]∂L

= w2U cCC : w is constant, and increasing L by 1 changes marginal utility of

consumption as though consumption increased by w.

• .∂[Uc

HHL]∂L

= U cHH(HL)

2 + U cH ·HLL: Using the product rule, bearing in mind that U c

H is

itself a function of H.

Multiplying and dividing the whole expression by w, the parameter of interest is:

∂L

∂t= −

1

w·

w2 · U cCC

w2 · U cCC + (HL)2 · U c

HH + U cHHLL

(A8)

53

This means that − 1w

< ∂L∂t

< 0. The child always withdraws labour earnings at a slower rate

than transfers are received. Hence, in the Nash or parent-leading Stackelberg model, child’s

consumption is strictly increasing in cash transfers.

A.3.2 The ‘tax’ rate

The parent’s first-order condition is:

[.] = −UpP + U

pC = 0 (A9)

The parameter of interest is therefore equal to:

∂t

∂L= −

[∂[.]∂L

]

[∂[.]∂t

](A10)

= −−

∂UpP

∂L+

∂UpC

∂L

−∂U

pP

∂t+

∂UpC

∂t

The elements of this expression are as follows:

• .∂U

pP

∂L= 0: Child’s labour supply has no effect on parent’s consumption.

• .∂U

pC

∂L= w · U

pCC : Increasing consumption by 1 means U

pC changes by U

pCC , so at the

margin, increasing consumption by w means UpC changes by w.U

pCC .

• .∂U

pP

∂t= −U

pPP : Increasing t by 1 has same effect as reducing own consumption by 1.

• .∂U

pC

∂t= U

pCC : Increasing t by 1 has same effect as increasing child’s consumption by 1.

This means the parameter of interest is:

∂t

∂L= −w ·

UpCC

UpPP + U

pCC

(A11)

This can be expressed as the ‘tax’ rate, in response to earnings rather than labour supply:

∂t

∂L·1

w= −

UpCC

UpPP + U

pCC

(A12)

The denominator here is more negative than numerator, so the expression is strictly between

zero and minus 1: the ‘tax rate’ is strictly between 0 and 100%. This means that in the Nash

54

or child-leading Stackelberg model, the parent withdraws transfers at a rate slower than wages

are earned, so the child’s consumption is strictly increasing in his labour supply.

55

A.4 Differentiated labour markets by gender

A.4.1 Job types

The LSYPE does not provide information on the types of jobs teenagers do. Howieson et al.

(2006) indicate the extent to which boys’ and girls’ labour markets are differentiated in Scot-

land, where the education system, labour market conditions and legislation are very similar to

England. The largest categories of employment among those aged 14 and under are newspaper

delivery (32% of workers, among which boys outnumber girls by a factor of five) and babysitting

(11% of workers, among which girls outnumber boys by a factor of six). In both cases, the gen-

der bias is partly driven by differences in physical and mental attributes affecting individuals’

ability to do the job well, but also by social norms for gender roles. This suggests that the size

and male dominance of the market for newspaper delivery is responsible for the higher male

employment at age 13-14, when few other jobs are available.

The largest categories of employment among 15 and 16 year olds are “cafes and restaurants”

(17.5%), “other shops” (14%) and “chain stores” (12%), with females more heavily concentrated

in these industries than males. Jobs in these categories are also likely to be restricted to 16 year-

olds in law (due to health and safety requirements in food preparation or the sale of alcohol) or

15 year-olds in practice (because this enables an eight hour shift to be supplied on a Saturday).

A.4.2 Gender roles and ethnicity

Table A5 shows that the overall trends in employment are driven by the majority white ethnic

group, who also have the highest employment levels for both sexes at every wave. There is

considerable variation in employment rates and trajectories among the other ethnic groups.

This will reflect a combination of socio-cultural norms, prior educational performance, poorer

labour market opportunities and active labour market discrimination, but also rigid gender

roles within certain ethnic groups which make employment among girls exceptionally rare. In

particular, Pakistani and Bangladeshi girls are almost completely excluded from the labour

market. This makes it sensible to estimate our models separately for boys and girls.19

19In both the parent-leading and child-leading specifications several ethnicity dummies are statistically signif-icant in both transfer and labour supply equations. Ethnicity therefore makes a difference in levels. However,by re-estimating on white students only and obtaining very similar results, we find no evidence for significantethnicity interactions with the parameters of interest.

56

Table A5: Employment rates by wave, sex and ethnicity



White 25.7% 21.3% *** 31.4% 30.3% 30.8% 34.8% ###

Mixed 15.7 % 16.0% 15.6% 19.9% 24.5% 20.5%

Indian 9.4% 4.4% *** 12.1% 5.0% *** 10.1% 3.4% ***

Pakistani 7.0% <1.5% *** 6.4% <1.5% *** 8.0% <1.5% ***

Bangladeshi 4.5% <1.5% *** 5.8% <1.5% *** 7.2% 3.1% *

Black Caribbean 11.2% 9.6% 11.5% 10.7% 12.1% 14.7%

Black African 7.8% 4.7% 10.1% 5.2% 6.0% 8.7%

Other 15.3% 9.8% 16.7% 8.1% 12.8% 11.1%

Symbols: *, **, ***: Boys’ employment higher than girls’ at 5%, 1% and 0.1% levels respectively. #, ##, ###: Girls’ employmenthigher than boys’ at 5%, 1% and 0.1% levels respectively. Standard errors clustered by school. Population proportions calculated using finalprobability weights.

57

A.5 Distinguishing household and market work

We do not observe job types but have assumed that the question on labour supply is interpreted

as referring to market work. We assume that this includes informal employment in the parent’s

own business, and that survey respondents distinguish the payments they receive for this work

from pocket money or allowances. However, it is possible that teenagers may regard babysitting

within as well as outside the household as ‘paid work’, yet double-count the payment they receive

as part of their reported transfers. If this is true the observed labour supply response (parent-

leading model) or parent’s ‘tax rate’ (child-leading model) will be positively biased (less negative

or more positive than the true effect).

We test this hypothesis by re-estimating the model for children with no younger siblings, for

whom there is no possibility of babysitting within the household. The key results are shown

in table A6. The coefficient on receiving cash transfers for girls in wave 1 of the parent-

leading model becomes less positive and insignificantly different from zero. The coefficient for

boys has become more negative (though the change is less drastic) and is now statistically

significant. These results lend qualified support to our initial rejection of the parent-leading

Stackelberg model based on 13-14 year-old girls’ apparent positive labour supply response to

parental transfers being due to this babysitting hypothesis. However, the parent’s significant

positive transfer response to both the IMD and month of birth means these results are still

inconsistent with the parent-leading Stackelberg model.

In the child-leading model, the wave 1 labour supply of daughters with no younger siblings

appears to be associated with a small ‘subsidy’, or increase in probability of transfers. This

finding at face value rejects the babysitting hypothesis, but this coefficient is very imprecisely

estimated and not statistically different from zero or the pooled-sample coefficient. The coeffi-

cients on cash transfers or labour supply do not change significantly either for boys or for older

girls (for whom we assume this matters less - see discussion in Appendix A.4, above), though

the conclusion drawn would change: statistically significant ‘tax rates’ are now observed in wave

2 rather than wave 3. It is possible that as children with ‘no younger siblings’ are more likely to

have ‘some older siblings’ than the pooled sample, this reflects parents having a softer attitude

towards labour supply in the final year of school, once they have seen how older siblings coped.

58

Table A6: Estimation results for sample members with no younger siblings.

Boys

Parent-leading Child-leading

Wave 1 Wave 1 Wave 2 Wave 3

Transfer Work Hours Work Hours Transfer Work Hours Transfer Work Hours Transfer(FIML 1st) (FIML 2nd) (FIML 1st) (FIML 2nd) (FIML 1st) (FIML 2nd) (FIML 1st) (FIML 2nd)

Transfer . -3.072* . . . . . .. (1.787) . . . . . .

Work Hours . . . -0.009 . -0.013* . -0.003. . . (0.008) . (0.007) . (0.007)

‘Permanent’ income 0.121** . -1.244 0.095* -1.231 0.118** 3.412 -0.081percentile (0.059) . (1.494) (0.056) (1.760) (0.059) (2.072) (0.065)

IMD (standardized) 0.009 -0.942*** -0.994*** . -0.688* . -0.936* .(0.016) (0.367) (0.342) . (0.394) . (0.539) .

Birth month -0.004 -0.113 -0.104 . -0.104* . -0.233* .(0.004) (0.085) (0.088) . (0.096) . (0.147) .

LEA age 16-64 0.016 0.028 -0.004 . -0.583* . -0.678* .unemployment rate (0.012) (0.271) (0.275) . (0.312) . (0.373) .

Joint significance of labourmarket variables: χ2

3. 11.88 13.03 . 11.59 . 11.98 .

(p-value) . (0.008) (0.005) . (0.009) . (0.008) .

Observations 1881 1881 1881 1881

Girls

Parent-leading Child-leading

Wave 1 Wave 1 Wave 2 Wave 3

Transfer Work Hours Work Hours Transfer Work Hours Transfer Work Hours Transfer(FIML 1st) (FIML 2nd) (FIML 1st) (FIML 2nd) (FIML 1st) (FIML 2nd) (FIML 1st) (FIML 2nd)

Transfer . 2.592 . . . . . .. (3.714) . . . . . .

Work Hours . . . 0.010 . -0.018* . -0.009. . . (0.010) . (0.009) . (0.007)

‘Permanent’ income 0.088* . 1.004 0.066 -1.478 0.117** -1.168 0.083percentile (0.052) . (1.435) (0.054) (1.502) (0.009) (1.680) (0.057)

IMD (standardized) 0.028** -0.907** -0.697* . -0.240 . -1.107* .(0.014) (0.444) (0.395) . (0.395) . (0.490) .

Birth month 0.007* -0.279*** -0.223*** . -0.098 . -0.386** .(0.004) (0.093) (0.086) . (0.080) . (0.123) .

LEA age 16-64 -0.006 -0.558* -0.596** . -1.074*** . -1.092*** .unemployment rate (0.010) (0.312) (0.295) . (0.329) . (0.317) .

Joint significance of labourmarket variables: χ2

3. 23.17 22.38 . 16.35 . 28.09 .

(p-value) . (0.000) (0.000) . (0.001) . (0.000) .

Observations 1915 1915 1915 1916

Notes: Joint significance statistics and p-values are Wald test statistics. Coefficients in transfer column presented as average marginal effectson the probability of a positive transfer being made presented in accompanying graphs). Standard errors, clustered by school, in parentheses.Longitudinal weights applied. *: p < 0.1; **: p < 0.05; ***: p < 0.01. Index of multiple deprivation is standardized by substractingthe mean and dividing by standard deviation. Month-of-birth within academic year: Sept (oldest in year) = 1, Aug (youngest in year) =12. Prior educational performance is Additional controls: Parent’s socio-economic status, parents’ employment, child’s prior educationalperformance (standardized average point score at age 11 - Key Stage 2 - in wave 1 and age 14 - Key Stage 3 - in waves 2 and 3), residentand non-resident siblings, lone parent family, step family, parent’s ill health limits activities, household own’s home (morgage or outright),child’s special educational needs (SEN) classification, urban-rural classification, child’s ethnicity, timing of interview.

59

A.6 Complete estimation output

The complete maximum likelihood estimation output for the parent-leading Stackelberg model

is shown in Tables A7-A8, and the child-leading Stackelberg model in Tables A9-A10, starting

overleaf. Tables 4-7 in the main body presented average marginal effects on the probability of

transfer for a set of key variables. Here we show the probit linear latent regression coefficients for

both dependent and all explanatory variables. We omit the output for the baseline specifications

assuming that transfers and labour supply are exogenous in the second stage of the parent-

leading and child-leading specifications respectively.

60

Tab

leA7:

Com

plete

max

imum

likelihoodestimationresults:

Parent-lead

ingmodel

Boys

Girls

Wave1

Wave2

Wave3

Wave1

Wave2

Wave3

tran

sfer

WorkHou

rstran

sfer

Work

Hou

rstran

sfer

WorkHou

rstran

sfer

Work

Hours

transfer

Work

Hours

transfer

Work

Hours

Transfer

-0.852

-7.299

**-15.14

6***

6.950**

-10.233***

-11.126**

(2.213

)(3.676

)(1.877

)(2.984)

(2.043)

(5.293)

‘Perman

ent’

income

0.44

6***

0.45

4***

0.22

8*0.31

4**

0.424***

0.387**

percentile

(0.132

)(0.134

)(0.133

)(0.144

)(0.137)

(0.169)

IMD

(standardized

)0.03

0-0.854

***

0.04

9-0.952

***

0.08

8**

-0.917

***

0.06

1*-0.952***

0.029

-0.330

0.094**

-0.356

(0.041

)(0.211

)(0.035

)(0.271

)(0.035

)(0.327

)(0.036

)(0.279)

(0.037)

(0.265)

(0.039)

(0.322)

Birth

mon

th-0.002

-0.075

0.01

5*-0.016

0.01

1-0.290

***

0.00

9-0.146**

-0.007

-0.097*

0.029***

-0.300***

(0.009

)(0.052

)(0.008

)(0.054

)(0.010

)(0.091

)(0.009

)(0.070)

(0.008)

(0.054)

(0.010)

(0.085)

LEA

age16

-64

0.07

3**

-0.155

0.08

7***

-0.357

*0.09

5***

-0.523

**0.02

1-0.552**

0.075**

-0.690***

0.096***

-0.742***

unem

ploymentrate

(0.029

)(0.185

)(0.028

)(0.201

)(0.026

)(0.225

)(0.029

)(0.234)

(0.031)

(0.229)

(0.029)

(0.263)

Prior

education

alperform

ance

KS3(age

14)pointscore

-0.011

-0.021

-0.004

-0.131

0.000

0.720***

0.014

0.529**

(standardized

)(0.027

)(0.236

)(0.029

)(0.281

)(0.030)

(0.225)

(0.032)

(0.254)

KS2(age

11)pointscore

0.01

00.26

6-0.025

0.604***

(standardized

)(0.031

)(0.186

)(0.033

)(0.218)

Parents’em

ployment:

TwoFT

-0.028

1.10

1-0.226

**1.85

0**

0.07

81.76

1-0.106

1.807**

-0.070

1.794**

0.056

3.500**

(0.126

)(0.785

)(0.112

)(0.849

)(0.178

)(1.584

)(0.120

)(0.835)

(0.112)

(0.809)

(0.191)

(1.653)

oneFT,on

ePT

-0.019

1.23

4-0.102

2.35

0***

0.08

61.04

2-0.060

1.227

-0.069

1.653**

0.114

3.135*

(0.121

)(0.762

)(0.108

)(0.781

)(0.178

)(1.604

)(0.116

)(0.868)

(0.105)

(0.781)

(0.186)

(1.657)

OneFT

only

-0.012

0.74

5-0.101

1.35

6*0.06

30.70

60.01

40.811

-0.081

0.326

0.078

1.352

(0.104

)(0.684

)(0.099

)(0.755

)(0.158

)(1.426

)(0.099

)(0.772)

(0.097)

(0.764)

(0.172)

(1.521)

One/tw

oPT,noFT

0.14

71.12

40.03

70.96

50.21

01.57

40.04

50.541

-0.055

0.530

0.095

0.602

(0.117

)(0.760

)(0.109

)(0.835

)(0.157

)(1.464

)(0.107

)(0.872)

(0.104)

(0.774)

(0.172)

(1.485)

Non

-resident

-0.015

-0.012

-0.004

0.20

1-0.020

0.22

7-0.017

0.318

-0.024

0.438**

-0.044

-0.297

siblings

(0.031

)(0.166

)(0.022

)(0.162

)(0.023

)(0.217

)(0.033

)(0.238)

(0.023)

(0.183)

(0.027)

(0.218)

Residentsiblings

-0.055

**0.55

5***

-0.031

0.32

5**

-0.064

***

0.42

4**

-0.115

***

1.038***

-0.098***

0.581***

-0.075***

0.318

(0.024

)(0.138

)(0.023

)(0.159

)(0.022

)(0.202

)(0.025

)(0.227)

(0.028)

(0.201)

(0.024)

(0.211)

Parents’ed

ucation

Degree

-0.002

-0.583

0.16

9-1.444

*0.08

8-0.559

-0.021

0.279

0.167

2.127**

0.276**

2.504**

(0.107

)(0.695

)(0.106

)(0.871

)(0.102

)(0.985

)(0.115

)(0.896)

(0.109)

(0.830)

(0.110)

(0.975)

A-Levels

-0.030

0.15

80.09

6-0.114

0.01

10.18

8-0.167

*0.214

-0.014

1.979***

0.012

2.376***

(0.092

)(0.589

)(0.089

)(0.745

)(0.088

)(0.859

)(0.096

)(0.799)

(0.093)

(0.752)

(0.090)

(0.812)

GCSEs

-0.046

0.13

40.09

30.14

9-0.063

0.63

0-0.186

**0.761

-0.082

2.052***

-0.006

2.632***

(0.090

)(0.575

)(0.082

)(0.741

)(0.082

)(0.876

)(0.089

)(0.809)

(0.088)

(0.725)

(0.089)

(0.798)

Other

qualification

s-0.364

*1.75

2-0.123

2.13

3-0.305

0.01

7-0.177

0.061

-0.140

-0.447

0.136

2.264

(0.212

)(1.356

)(0.193

)(1.450

)(0.188

)(2.149

)(0.203

)(1.728)

(0.185)

(1.638)

(0.222)

(2.007)

Parents’SES

NSSEC

1-2

0.03

0-0.675

*0.00

8-0.210

0.07

60.37

40.14

2**

-1.105**

-0.007

-0.487

0.052

0.161

(0.070

)(0.385

)(0.062

)(0.376

)(0.060

)(0.533

)(0.064

)(0.529)

(0.061)

(0.422)

(0.063)

(0.487)

NSSEC

30.13

7-0.706

0.03

4-1.578

**0.19

5**

-0.412

0.03

7-0.753

0.024

-0.800

0.039

0.831

(0.091

)(0.578

)(0.091

)(0.650

)(0.096

)(0.859

)(0.092

)(0.661)

(0.095)

(0.709)

(0.097)

(0.762)

NSSEC

4(self-

-0.235

***

0.04

9-0.128

-0.114

-0.001

0.47

40.06

90.740

0.036

1.385**

0.021

1.610**

employed)

(0.085

)(0.464

)(0.085

)(0.599

)(0.095

)(0.785

)(0.080

)(0.577)

(0.089)

(0.639)

(0.092)

(0.712)

NSSEC8imp

-0.068

-0.530

0.06

8-1.336

-0.047

-0.287

-0.003

-0.408

0.028

0.033

0.155

0.946

(0.136

)(0.963

)(0.139

)(1.177

)(0.140

)(1.294

)(0.129

)(1.381)

(0.128)

(1.254)

(0.158)

(1.410)

Lon

eparent

0.05

4-0.061

0.08

10.30

1-0.014

-0.535

-0.027

1.144*

0.116

0.977*

0.152*

1.726***

(0.081

)(0.493

)(0.072

)(0.524

)(0.074

)(0.670

)(0.086

)(0.632)

(0.074)

(0.524)

(0.078)

(0.628)

Observations

4854

4854

4854

4846

4846

4846

Notes:*:p<

0.1;**:p<

0.05

***:p<

0.01.Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.

61

Tab

leA8:

Com

plete

max

imum


Parent-lead

ingmodel

(continued

)

Boys

Girls

Wave1

Wave2

Wave3

Wave1

Wave2

Wave3

tran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rs

You

th’s

ethnicity

Mixed

race

-0.026

-3.013***

0.100

-2.401**

0.032

-2.048**

-0.112

-0.136

-0.053

-0.149

-0.117

-1.567

(0.132)

(0.940)

(0.121)

(1.148)

(0.119)

(0.940)

(0.128)

(0.922)

(0.142)

(0.889)

(0.132)

(1.093)

Indian

-0.549***

-3.725***

-0.423***

-5.036***

-0.355***

-7.292***

-0.633***

-3.738**

-0.576***

-8.796***

-0.313***

-10.703***

(0.096)

(0.836)

(0.093)

(1.062)

(0.101)

(1.293)

(0.111)

(1.472)

(0.102)

(1.100)

(0.106)

(1.395)

Pak

istanior

0.143

-6.182***

0.113

-6.802***

0.297**

-6.688***

0.072

-9.158***

0.083

-12.876***

0.061

-11.102***

Ban

glad

eshi

(0.112)

(0.880)

(0.119)

(1.029)

(0.124)

(1.370)

(0.113)

(1.487)

(0.109)

(2.097)

(0.116)

(1.478)

Black

African

or-0.068

-2.049*

0.043

-2.456*

-0.035

-4.948**

-0.031

-1.726*

-0.078

-3.010***

0.242**

-3.252***

Caribbean

(0.127)

(1.240)

(0.142)

(1.325)

(0.136)

(1.944)

(0.108)

(0.940)

(0.111)

(1.039)

(0.120)

(1.078)

Other

0.005

0.163

-0.171

-2.334

0.060

-3.420*

-0.344*

-1.340

-0.518***

-4.484**

-0.505***

-7.416***

(0.206)

(1.203)

(0.190)

(1.498)

(0.201)

(1.988)

(0.182)

(1.566)

(0.158)

(1.925)

(0.159)

(2.148)

SpecialEd’Needs

-0.097

-0.432

-0.026

-0.914*

-0.047

-1.071*

-0.064

-0.335

0.003

-0.965

-0.054

-2.141***

(0.066)

(0.438)

(0.064)

(0.517)

(0.067)

(0.638)

(0.084)

(0.687)

(0.080)

(0.642)

(0.081)

(0.698)

Tow

nor

Village

-0.007

-0.154

-0.089

0.865*

-0.012

1.264**

-0.117*

1.580***

-0.217***

1.479***

-0.193***

1.663***

(0.071)

(0.377)

(0.066)

(0.463)

(0.064)

(0.537)

(0.069)

(0.521)

(0.066)

(0.420)

(0.064)

(0.533)

Isolated

area

-0.256*

-0.110

-0.224*

0.554

-0.454***

0.392

-0.045

1.130

-0.219*

2.749***

-0.047

3.054***

(0.145)

(0.743)

(0.120)

(0.965)

(0.124)

(1.115)

(0.127)

(0.952)

(0.128)

(0.732)

(0.141)

(0.884)

Illhealthlimits

0.154**

0.147

0.083

0.101

0.058

-0.009

-0.049

-0.189

0.039

-0.819**

0.026

-0.073

parent’sactivities

(0.068)

(0.405)

(0.068)

(0.503)

(0.062)

(0.552)

(0.062)

(0.483)

(0.059)

(0.413)

(0.065)

(0.513)

Hom

eow

ner

(mortgage

-0.063

0.058

0.105

0.513

-0.092

-0.150

-0.031

-0.580

-0.051

0.044

0.058

0.329

oroutright)

(0.066)

(0.430)

(0.066)

(0.517)

(0.065)

(0.622)

(0.074)

(0.519)

(0.068)

(0.485)

(0.073)

(0.548)

StepFam

ily

0.106

-0.099

0.081

-0.079

-0.007

-0.050

0.129

-0.094

-0.003

0.018

-0.084

-0.317

(0.075)

(0.472)

(0.072)

(0.523)

(0.067)

(0.645)

(0.081)

(0.607)

(0.075)

(0.506)

(0.072)

(0.592)

Not

Greater

Lon

don

-0.161*

2.081***

-0.064

1.234

-0.099

2.073**

0.078

1.908***

0.105

2.689***

0.116

1.239*

(0.086)

(0.681)

(0.096)

(0.767)

(0.093)

(0.831)

(0.087)

(0.721)

(0.078)

(0.778)

(0.084)

(0.733)

Tim

eof

interview

March

-0.093

0.175

-0.042

0.225

-0.037

-0.480

-0.032

0.502

0.043

1.835**

-0.073

-0.732*

(0.065)

(0.376)

(0.127)

(0.868)

(0.054)

(0.452)

(0.068)

(0.512)

(0.125)

(0.873)

(0.054)

(0.406)

April

-0.056

0.353

-0.110

0.248

-0.055

0.712

-0.029

0.391

0.013

2.202**

0.002

1.093

(0.067)

(0.433)

(0.126)

(0.890)

(0.081)

(0.727)

(0.073)

(0.532)

(0.124)

(0.869)

(0.077)

(0.692)

May

-0.057

0.908*

-0.123

0.159

-0.287**

-2.224

-0.068

1.305**

0.068

1.895**

-0.311***

-1.883

(0.088)

(0.519)

(0.129)

(0.934)

(0.142)

(1.497)

(0.092)

(0.641)

(0.126)

(0.898)

(0.118)

(1.180)

June

-0.089

1.115

-0.170

1.185

-0.241

-1.256

-0.061

1.142

-0.074

1.440

-0.288

2.429

(0.111)

(0.873)

(0.137)

(0.989)

(0.206)

(2.172)

(0.127)

(1.096)

(0.133)

(0.982)

(0.208)

(1.692)

July

0.194

0.654

0.061

1.370

-0.091

.0.029

0.380

-0.041

2.140

0.092

1.595

(0.152)

(0.855)

(0.204)

(1.318)

(0.637)

.(0.158)

(1.120)

(0.205)

(1.683)

(0.625)

(2.683)

After

birthday

-0.166**

0.182

0.071

0.386

0.029

-0.308

0.052

-0.123

-0.063

-0.460

0.087

-0.410

(0.073)

(0.486)

(0.079)

(0.589)

(0.075)

(0.709)

(0.079)

(0.596)

(0.079)

(0.497)

(0.077)

(0.635)

Observations

4854

485

44854

4846

4846

4846

Notes:*:p<

0.1;**:p<

0.05

***:p<

0.01.Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.

62

Tab

leA9:

Com

plete

max

imum


Child-leadingmodel

Boys

Girls

Wave1

Wave2

Wave3

Wave1

Wave2

Wave3

tran

sfer

WorkHours

transfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rs

Work

Hou

rs-0.018

-0.033*

-0.023

-0.008

-0.031

-0.055***

(0.022)

(0.017)

(0.015)

(0.026)

(0.022)

(0.017)

‘Perman

ent’

income

0.381***

0.341

0.347**

-1.299

0.181

-0.375

0.333**

-0.124

0.355**

-1.664*

0.322**

-0.641

percentile

(0.135)

(0.915)

(0.137)

(1.016)

(0.130)

(1.285)

(0.148)

(0.988)

(0.140)

(1.007)

(0.146)

(1.194)

IMD

(standardized)

-0.830***

-1.034***

-1.178***

-0.786***

-0.389

-0.582*

(0.207)

(0.268)

(0.317)

(0.238)

(0.257)

(0.320)

Birth

mon

th-0.076

-0.040

-0.331***

-0.120*

-0.078

-0.393***

(0.052)

(0.053)

(0.089)

(0.064

)(0.051)

(0.083)

LEA

age16-64

-0.122

-0.499**

-0.843***

-0.489**

-0.849***

-1.018***

unem

ploymentrate

(0.185)

(0.202)

(0.223)

(0.203)

(0.219)

(0.232)

Prioreducation

alperform

ance

KS3(age

14)pointscore

-0.021

0.014

-0.019

-0.125

0.007

0.744***

0.002

0.483*

(standardized)

(0.028)

(0.234)

(0.030)

(0.275)

(0.032)

(0.213)

(0.033)

(0.258)

KS2(age

11)pointscore

0.015

0.256

-0.026

0.553***

(standardized)

(0.032)

(0.187)

(0.033)

(0.200)

Parents’em

ployment:

TwoFT

-0.017

0.984

-0.166

2.430***

0.036

1.365

-0.122

1.814**

-0.023

2.118**

0.087

3.371**

(0.126)

(0.839)

(0.110)

(0.907)

(0.178)

(1.508)

(0.119)

(0.801)

(0.113

)(0.896)

(0.193)

(1.617)

OneFT,on

ePT

-0.019

1.147

-0.064

2.649***

0.014

0.610

-0.080

1.302

-0.044

1.958**

0.121

2.855*

(0.122)

(0.792)

(0.104)

(0.837)

(0.180)

(1.494)

(0.115)

(0.809)

(0.104

)(0.832)

(0.188)

(1.617)

OneFT

only

-0.005

0.679

-0.067

1.632**

0.033

0.344

0.002

0.980

-0.071

0.632

0.041

1.211

(0.105)

(0.707)

(0.098)

(0.783)

(0.159)

(1.343)

(0.096)

(0.685)

(0.099

)(0.778)

(0.172)

(1.477)

One/tw

oPT,noFT

0.141

1.078

0.050

0.891

0.168

0.668

0.040

0.711

-0.052

0.657

0.021

0.482

(0.119)

(0.763)

(0.107)

(0.834)

(0.157)

(1.391)

(0.108)

(0.750)

(0.105

)(0.761)

(0.176)

(1.452)

Non

-resident

-0.015

-0.004

0.003

0.207

-0.019

0.342

-0.017

0.252

-0.023

0.538***

-0.038

-0.159

siblings

(0.030)

(0.169)

(0.022)

(0.166)

(0.023)

(0.212)

(0.034)

(0.202)

(0.023)

(0.184)

(0.026)

(0.227)

Residentsiblings

-0.052**

0.566***

-0.020

0.410**

-0.055**

0.723***

-0.111***

0.750***

-0.097***

0.902***

-0.065***

0.587***

(0.024)

(0.135)

(0.023)

(0.160)

(0.023)

(0.198)

(0.025)

(0.157)

(0.028

)(0.175)

(0.025)

(0.168)

Parents’education

Degree

-0.037

-0.608

0.098

-1.742**

0.021

-1.024

-0.056

0.300

0.149

1.762**

0.264**

1.594*

(0.107)

(0.709)

(0.105)

(0.865)

(0.103)

(0.970)

(0.116)

(0.809)

(0.111

)(0.795)

(0.112)

(0.932)

A-Levels

-0.061

0.164

0.047

-0.275

-0.032

0.055

-0.187*

-0.167

-0.020

2.033***

0.018

2.309***

(0.093)

(0.593)

(0.088)

(0.755)

(0.089)

(0.836)

(0.097)

(0.695)

(0.094

)(0.733)

(0.092)

(0.813)

GCSEs

-0.068

0.165

0.060

-0.021

-0.079

0.867

-0.194**

0.295

-0.079

2.289***

-0.002

2.688***

(0.091)

(0.573)

(0.082)

(0.746)

(0.082)

(0.863)

(0.089)

(0.676)

(0.090

)(0.704)

(0.090)

(0.796)

Other

qualification

s-0.371*

1.917

-0.130

2.452*

-0.292

1.459

-0.198

-0.462

-0.132

-0.143

0.142

1.749

(0.212)

(1.342)

(0.185)

(1.435)

(0.182)

(2.122)

(0.202)

(1.506)

(0.187

)(1.674)

(0.220)

(1.926)

Parents’SES

NSSEC

1-2

0.015

-0.723*

0.009

-0.187

0.046

0.041

0.128**

-0.582

-0.026

-0.437

0.006

-0.054

(0.070)

(0.398)

(0.062)

(0.387)

(0.059)

(0.543)

(0.063)

(0.411)

(0.061

)(0.418)

(0.063)

(0.480)

NSSEC

30.137

-0.747

0.025

-1.657**

0.185*

-1.277

0.022

-0.593

-0.026

-0.818

0.044

0.649

(0.092)

(0.565)

(0.092)

(0.655)

(0.096)

(0.869)

(0.092)

(0.561)

(0.095

)(0.667)

(0.101)

(0.759)

NSSEC

4(self-

-0.254***

0.127

-0.144*

0.224

-0.053

0.550

0.062

0.977*

0.017

1.305**

0.016

1.533**

employed

(0.083)

(0.458)

(0.084)

(0.580)

(0.097)

(0.783)

(0.081)

(0.502)

(0.091)

(0.601)

(0.095)

(0.729)

NSSEC

8(lon

g--0.039

-0.513

0.078

-1.543

-0.080

-0.070

0.023

-0.308

0.062

-0.159

0.117

0.578

term

unem

ployed)

(0.136)

(0.971)

(0.141)

(1.184)

(0.137)

(1.243)

(0.122)

(1.328)

(0.128)

(1.242)

(0.154)

(1.349)

Lon

eparent

0.035

-0.023

0.066

0.080

-0.022

-0.471

-0.028

0.964*

0.122

0.617

0.172**

1.353**

(0.080)

(0.516)

(0.073)

(0.539)

(0.077)

(0.701)

(0.087)

(0.566)

(0.076

)(0.528)

(0.079)

(0.640)

Observation

s4854

4854

4854

4846

4846

4846

Notes:*:p<

0.1;**:p<

0.05

***:p<

0.01.Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.

63

Tab

leA10

:Com

plete

max

imum


Child-leadingmodel

(continued

)

Boys

Girls

Wave1

Wave2

Wave3

Wave1

Wave2

Wave3

tran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rstran

sfer

WorkHou

rs

You

th’s

ethnicity

Mixed

race

-0.023

-3.032***

0.109

-2.617**

0.074

-2.247**

-0.094

-0.437

-0.023

-0.055

-0.035

-1.346

(0.132)

(0.948)

(0.125)

(1.126)

(0.128)

(0.978)

(0.132)

(0.755)

(0.139)

(0.860)

(0.122)

(1.200)

Indian

-0.520***

-3.602***

-0.410***

-4.029***

-0.326***

-5.698***

-0.619***

-5.734***

-0.573***

-7.132***

-0.360***

-9.613***

(0.096)

(0.685)

(0.093)

(0.964)

(0.102)

(1.068)

(0.112)

(1.216)

(0.105)

(1.045)

(0.112)

(1.222)

Pak

istanior

0.157

-6.248***

0.108

-7.117***

0.301**

-7.575***

0.114

-9.147***

0.115

-13.012***

0.092

-11.396***

Ban

glad

eshi

(0.113)

(0.890)

(0.124)

(1.040)

(0.133)

(1.275)

(0.114)

(1.483)

(0.114)

(2.094)

(0.117)

(1.439)

Black

African

or-0.001

-2.087*

0.069

-2.564*

0.090

-5.208**

0.018

-1.844**

-0.013

-2.882***

0.304**

-3.886***

Caribbean

(0.120)

(1.254)

(0.141)

(1.333)

(0.125)

(2.061)

(0.108)

(0.920)

(0.113)

(1.006)

(0.124)

(1.056)

Other

0.042

0.131

-0.163

-1.934

0.073

-3.706**

-0.342*

-2.447*

-0.507***

-3.038

-0.514***

-5.429***

(0.206)

(1.212)

(0.191)

(1.448)

(0.209)

(1.776)

(0.192)

(1.482)

(0.158)

(1.861)

(0.164)

(1.934)

SpecialEd’Needs

-0.091

-0.411

-0.035

-0.841

-0.065

-0.787

-0.057

-0.477

0.003

-0.993

-0.123

-1.937***

(0.067)

(0.441)

(0.064)

(0.522)

(0.067)

(0.623)

(0.085)

(0.614)

(0.081)

(0.623)

(0.082)

(0.687)

Tow

nor

Village

-0.077

-0.099

-0.164**

1.169***

-0.123*

1.546***

-0.161**

1.263***

-0.251***

2.159***

-0.243***

2.422***

(0.071)

(0.379)

(0.064)

(0.448)

(0.065)

(0.523)

(0.069)

(0.444)

(0.068)

(0.404)

(0.065)

(0.456)

Isolated

area

-0.323**

0.013

-0.279**

1.190

-0.533***

3.036***

-0.082

1.011

-0.245*

3.486***

-0.077

3.287***

(0.146)

(0.724)

(0.122)

(0.892)

(0.124)

(1.080)

(0.127)

(0.836)

(0.130)

(0.721)

(0.146)

(0.859)

Illhealthlimits

0.153**

0.126

0.072

-0.072

0.043

-0.187

-0.048

-0.335

0.030

-0.948**

0.038

-0.131

parent’sactivities

(0.068)

(0.417)

(0.067)

(0.504)

(0.062)

(0.545)

(0.062)

(0.425)

(0.061)

(0.410)

(0.066)

(0.532)

Hom

eow

ner

(mortgage

-0.065

0.047

0.102

0.316

-0.108*

0.221

-0.064

-0.609

-0.058

0.240

0.018

0.128

oroutright)

(0.064)

(0.438)

(0.067)

(0.505)

(0.063)

(0.634)

(0.071)

(0.458)

(0.069)

(0.480)

(0.070)

(0.547)

Stepfamily

0.096

-0.117

0.071

-0.263

-0.008

-0.081

0.135*

0.222

0.015

0.024

-0.091

-0.000

(0.075)

(0.464)

(0.072)

(0.515)

(0.068)

(0.631)

(0.081)

(0.490)

(0.077)

(0.507)

(0.073)

(0.536)

Not

GreaterLon

don

-0.176**

2.158***

-0.094

1.369*

-0.067

2.372***

0.080

2.099***

0.116

2.287***

0.128

0.929

(0.086)

(0.678)

(0.096)

(0.790)

(0.093)

(0.794)

(0.085)

(0.673)

(0.077)

(0.707)

(0.085)

(0.698)

Month

ofinterview:

March

-0.096

0.212

-0.046

0.316

-0.033

-0.329

-0.024

0.421

0.012

1.803**

-0.085

-0.522

(0.064)

(0.371)

(0.129)

(0.865)

(0.056)

(0.420)

(0.069)

(0.438)

(0.128)

(0.865)

(0.054)

(0.402)

April

-0.051

0.373

-0.101

0.497

-0.058

1.020

-0.023

0.309

0.008

2.189**

0.052

1.096

(0.067)

(0.434)

(0.128)

(0.867)

(0.080)

(0.718)

(0.073)

(0.462)

(0.130)

(0.874)

(0.078)

(0.674)

May

-0.054

0.932*

-0.092

0.403

-0.318**

-0.671

-0.041

1.181**

0.062

1.742*

-0.306***

-0.776

(0.086)

(0.524)

(0.131)

(0.924)

(0.139)

(1.260)

(0.091)

(0.535)

(0.131)

(0.896)

(0.118)

(1.098)

June

-0.083

1.168

-0.120

1.564

-0.216

-0.159

-0.020

1.051

-0.087

1.709*

-0.145

3.388*

(0.111)

(0.887)

(0.138)

(0.974)

(0.215)

(2.222)

(0.118)

(0.969)

(0.137)

(0.960)

(0.207)

(1.836)

July

0.194

0.634

0.155

1.242

-0.731

.0.058

0.472

-0.088

2.442

0.496

0.929

(0.151)

(0.862)

(0.202)

(1.349)

(0.744)

.(0.158)

(0.948)

(0.200)

(1.592)

(0.533)

(3.815)

After

Birthday

-0.149***

0.208

-0.012

0.280

-0.009

-0.406

-0.007

-0.015

-0.034

-0.237

-0.042

-0.684

(0.053)

(0.461)

(0.061)

(0.585)

(0.048)

(0.703)

(0.058)

(0.539)

(0.063)

(0.486)

(0.052)

(0.628)

Observations

4854

485

44854

4846

4846

4846

Notes:*:p<

0.1;**:p<

0.05

***:p<

0.01.Sta

ndard

errors,clu

stere

dby

school,

inpare

nth

ese

s.Longitudin

alweights

applied.

64

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